When Donald J. Trump huddled with Republican senators at a closed-door meeting in the Capitol days before his inauguration, Senator Rick Scott of Florida rose and gushed to him about the exhilarating opportunity the party had to “right-size” the federal government by slashing it mercilessly, a long-held conservative goal.

Mr. Trump brusquely agreed but quickly steered the conversation in a different direction, according to two people who attended the meeting. What he was really excited to discuss was tariffs, and he launched into a lengthy discourse about his plans, pulling out a paper from his jacket pocket and laying out calculations of potential revenue the nation could bring in from taxing imports.

The exchange underscored the chasm between Mr. Trump and many members of his party who are setting to work to push his agenda through a closely divided Congress. Even as Republicans have coalesced around broad fiscal policies like cutting spending and extending the tax cuts Mr. Trump enacted in 2017, many do not share his enthusiasm for several ideas he has proposed, including implementing broad tariffs and lowering the corporate tax rate.

Those disagreements are at the heart of Republican leaders’ efforts to piece together legislation carrying the bulk of Mr. Trump’s domestic policy agenda — a massive bill cutting taxes, slashing spending and slowing immigration that they plan to fast-track over the objections of Democrats. It will be a central topic of discussion this week as House Republicans convene in Miami for a retreat entitled “Delivering the America First Agenda.”

Mr. Trump is expected to address them Monday evening to kick off the gathering.

The president — who is famously vindictive and can count on a contingent of MAGA allies ready to hector and threaten any Republican who stands in his way — is likely to demand unbending loyalty from his party when it comes to domestic policy.

At a meeting with lawmakers this month at Fort McNair in Washington, Stephen Miller, Mr. Trump’s deputy chief of staff, described the major legislation taking shape in existential terms. His message, according to a person who attended the private session, was: You may not think the bill is perfect, but this is the be-all and end-all — and you will be with us.

While Republicans have traditionally agitated for less government spending, Mr. Trump has displayed a laissez-faire attitude toward cutting costs and proposed a number of policies that would actually increase the nation’s debt.

Some Republicans have privately made it clear that they’d rather not include some of Mr. Trump’s most expensive proposals in the legislation, especially as they battle concerns from hard-right Republicans that the bill will cost too much.

But Mr. Trump has personally been lobbying lawmakers on some of the issues he campaigned on. In a private meeting with Republican congressional leaders in the Cabinet Room at the White House on Wednesday, he urged them to implement his campaign promise to eliminate taxes on tips.

He told them repeatedly that he saw the move as a winning issue, according to two people familiar with his comments who were not authorized to discuss the private meeting.

Of the suite of tax cuts Mr. Trump proposed during the campaign, terminating taxes on tips has gained the most traction on Capitol Hill. The idea won bipartisan support during the campaign, and Republican aides are working on legislation that would translate the “no tax on tips” slogan into policy that won’t kick off a gold rush of tax avoidance.

There are several other promises Republicans would rather avoid. Free traders on Capitol Hill have particularly bristled at Mr. Trump’s vows to enact across-the-board tariffs. While the president has the authority to unilaterally impose tariffs, some Republicans have studied the possibility of imposing tariffs through law — an idea that quickly proved unpopular within the party.

Senator Rand Paul of Kentucky emerged from the closed-door meeting with Mr. Trump and the other Republican senators saying that the main way the president discussed paying for the massive reconciliation bill was through “big, beautiful tariffs.”

“I still don’t think tariffs are a good idea,” Mr. Paul said. “International trade has made the entire world incredibly prosperous, and if you look at G.D.P. per capita over the last 70 years, it’s a hockey stick going straight up. I think trade is a good thing, and international trade is a great thing, and it makes everybody richer.”

Despite the warnings from members of his own party on trade, Mr. Trump, who has been dispensing threats to close trading partners, is likely to move ahead with sweeping tariffs. Much of the rest of his campaign agenda — like making interest payments on car loans tax deductible — will require nearly unanimous support from his party in Congress.

Among Mr. Trump’s ideas is to lower the corporate tax rate to 15 percent for companies that make their products in the United States. While Republicans on Capitol Hill are throwing around different ideas for new manufacturing incentives, some in the party, and even some corporate lobbyists, hope to leave the rate at 21 percent. They worry that lowering it further would raise the cost of the bill and potentially imperil its passage.

“I think that digs us a deeper hole,” said Senator Thom Tillis, a member of the Finance Committee. “I’m sympathetic to it, but arguably I think if we were at a percentage point or two more we’d have been OK and had less of a revenue problem.”

Mr. Trump has not weighed in on many of his promised tax cuts publicly since he won the election, and he is still assembling the members of his team who will put forward the administration’s policy positions.

Some Republicans are waiting to see how hard the Trump administration actually pushes for proposals like eliminating taxes on overtime pay before digging too far into their specifics. Other pledges are already considered dead: Republican lawmakers and aides expect that exempting Social Security benefits from taxes would run afoul of procedural rules in the Senate and are preparing alternative ways to cut taxes for older Americans.

It is unclear how much dissent Mr. Trump will tolerate as the package comes together. Representative Marjorie Taylor Greene, a close ally of Mr. Trump and ultraconservative firebrand, urged her colleagues at a House hearing this week to commit themselves to the full sweep of Mr. Trump’s fiscal agenda.

“When I saw him and heard him campaign saying loudly ‘No tax on tips,’ ‘No tax on Social Security’ and ‘No tax on overtime,’ people rose to their feet and cheered loudly — standing ovation after standing ovation,” she said. “I promise you President Trump, especially for Republicans, is more popular than you are in your district.”

Mr. Trump recently invited more than a dozen House Republicans to visit him at Mar-a-Lago, his Florida estate, to discuss raising the $10,000 limit on the state and local tax deduction. The president endorsed raising the cap during the campaign, delighting Republicans from high-tax states like New York who have made doing so a political priority for years. At the Florida meeting, he asked the Republicans focused on the issue to come up with a compromise that could become law, according to lawmakers who attended.

But many in the party detest the state and local tax deduction, often called SALT, and would rather see it eliminated entirely than expanded. Republicans created the $10,000 limit in their 2017 tax law — which Mr. Trump signed — to help offset cost of the cuts they are now trying to extend.

“It’s a giveaway to the wealthy and the states that prioritize the woke agenda over good governance and it’s paid for by the hardworking taxpayers in states that do things right,” Representative Keith Self, a Republican from Texas, said.

Those divisions have left some Republican leaders convinced that the only way they will be able to quickly paper over longstanding policy disagreements is by rolling all the measures into one enormous bill, forcing lawmakers to go on the record in a single up-or-down vote on Mr. Trump’s agenda.

That would essentially dare Republicans to challenge the president, a move many have privately said they believe their colleagues are loath to make after Mr. Trump went after Representative Chip Roy of Texas last month for opposing his push to raise the debt limit.

The cease-fires in Gaza and Lebanon will most likely hold for now, despite being tested to their limits over the weekend, because all sides want to avoid full-scale fighting at least for a few weeks, analysts said.

In southern Lebanon, Israeli troops remained in position past the deadline on Sunday for their withdrawal, amid Israeli claims that Hezbollah had broken its own pledge to leave the area. In Gaza, Hamas failed to release a female hostage whom Israel had hoped would be freed on Saturday, prompting Israel to delay the agreed return of displaced Palestinians to their homes in northern Gaza.

But even as each side accused the other of reneging on their deals, analysts said, both Israel and its opponents had reasons to remain flexible and temporarily overlook the other’s transgressions.

Hezbollah, though angry at Israel for keeping troops in southern Lebanon, would risk a devastating Israeli counterattack if it renews its rocket strikes on Israeli cities. Hamas wants to retain power in Gaza and risks losing it if war returns. And Israel needs to maintain the current arrangement in Gaza long enough to free at least two dozen more hostages. Israeli leaders have also appeared eager to placate President Trump, who campaigned on a promise to keep peace in the Middle East.

Illustrating their desire to prolong the Gaza truce, Israel and Hamas seemed to resolve the weekend’s crisis close to midnight on Sunday. The government of Qatar, a mediator between the sides, said that the female hostage, Arbel Yehud, would be freed this week along with two others who would be released ahead of schedule. In return, Israel said that it would allow displaced Palestinians to return to northern Gaza on Monday morning.

As for Lebanon, the White House announced that the truce there would be extended until Feb. 18, though there was no immediate comment from Israel or Hezbollah. The Lebanese prime minister’s office confirmed the extension.

Aaron David Miller, a former U.S. negotiator in Middle East peace talks, said, “They’re going to get through the next few weeks — beyond that is anyone’s guess.”

“These are not agreements between the United States and Switzerland. They’re agreements that depend on each side giving the other a certain discretion and margin for maneuver,” he added. “That is their weakness, but also their strength.”

That wriggle room ultimately allowed both truces to survive the weekend, even as Israeli troops shot and killed people in both Lebanon and Gaza who were trying to return to areas still controlled by Israel.

The Lebanese Health Ministry said that 22 people had been killed by Israeli fire in southern Lebanon, and the Palestinian Authority’s news agency said that one person had been killed in Gaza as large crowds in both places gathered near Israeli troops, demanding to go home.

But by Monday morning, the standoff in Gaza appeared set to ease. In Lebanon, Hezbollah issued a statement praising the residents attempting to return and calling on foreign powers to force Israel to withdraw. But Hezbollah did not resume its rocket fire.

Analysts say that Hezbollah is unlikely to risk further losses while its leadership is decimated and its benefactor, Iran, is weakened. Also, the group’s main arms supply route, through Syria, was blocked in December when the Syrian president, Bashar al-Assad, an ally of Hezbollah, was ousted by rebels.

Hezbollah’s commanders do “still have some rockets, they have some guns, they can do something,” said Hanin Ghaddar, a Lebanese analyst at the Washington Institute for Near East Policy, a foreign affairs research group.

“But it’s suicidal if they do this, because they know that any kind of attack by Hezbollah in Israel means that Israel will take the opportunity to come back full blast and annihilate whatever is left of them,” Ms. Ghaddar added.

Hezbollah is also probably wary of losing support among its Shiite Muslim base, particularly in next year’s parliamentary elections, Ms. Ghaddar said. Lebanon’s Shiite community paid the largest price for Hezbollah’s decision to go to war with Israel in October 2023 in solidarity with its ally Hamas. Shiite villages and towns in southern Lebanon bore the brunt of Israel’s ensuing air campaign and ground invasion.

“If the Shia do not vote for them, this is the end of Hezbollah,” said Ms. Ghaddar, the author of a book about Hezbollah’s relationship with its base. “They cannot really do anything if they don’t know 100 percent that the Shia community is going to support it.”

Because Hezbollah is less likely to resume fighting, the Gaza cease-fire is considered the frailest of the two truces.

But its biggest stress test is not expected until the beginning of March, when Hamas and Israel must decide whether to extend the arrangement beyond an initial 42-day truce.

For now, Israel has signaled it wants to maintain the cease-fire to sustain the flow of hostage releases. But an extension would require both sides to agree to a permanent end to the war — a bridge that Prime Minister Benjamin Netanyahu of Israel has appeared unwilling to cross. Mr. Netanyahu’s coalition government relies on far-right lawmakers who seek permanent Israeli control of Gaza, and his administration could collapse if the war ends with Hamas still in charge.

The terms of the agreement allow for some flexibility. The truce can continue beyond the 42-day mark as long as both sides remain negotiating about whether to make the arrangement permanent.

But Israeli officials say they will not remain locked in endlessly fruitless negotiations, especially if Hamas stops releasing hostages. And Hamas is unlikely to keep freeing the hostages, its main bargaining chip, without an Israeli promise to cease hostilities permanently.

“Hamas wants a cease-fire but not at all costs,” said Mkhaimar Abusada, a Palestinian political scientist from Gaza. “They want a cease-fire that ends the war.”

Much could depend on President Trump’s willingness to cajole Mr. Netanyahu toward a more lasting truce. Mr. Trump’s private messages to the Israeli prime minister were crucial to the forging of the initial phase, but it remains to be seen whether the American president will maintain that position beyond a few weeks.

“If Netanyahu succeeds in convincing Trump of the need to renew the war, there’ll probably be a renewal of the war,” Mr. Abusada said. “If Trump keeps his promise that he doesn’t want any wars and he wants more peace — whether it’s in Gaza, Ukraine or all over the world — that’s a different thing.”