House Speaker Paul D. Ryan, (R.Wis.), right, and House Majority Whip Steve Scalise(R-La.) walk to the House floor for a vote at the U.S. Capitol on Monday. (Aaron P. Bernstein/Bloomberg News)

The deal that ended the government shutdown on Monday paved the way for Senate consideration of immigration legislation, but it did nothing to ensure that the House would act on such a bill — or that President Trump would sign it.

That has raised fears among immigrant advocates that the shutdown-ending compromise merely sets up a repeat of what happened five years ago, when eight senators forged an immigration deal that passed the Senate but went nowhere in the House after the GOP’s conservative base revolted against any attempt to give “amnesty” to illegal immigrants.

House conservatives predicted Monday that a Senate bill offering legal status to “dreamers” — immigrants who were brought to the United States illegally as children — could see a similar fate if it resembles the bipartisan proposals that have so far been put forward.

“Just like the Gang of Eight bill didn’t pass in the House, this idea is not going to pass in the House. That’s when they’re going to realize that they’re going to have to move a little bit to our side,” said Rep. Raúl R. Labrador (R-Idaho), a co-author of a conservative bill that would offer legal status to some dreamers, alongside a host of other policies.

One key obstacle is that the bipartisan group of senators that won a commitment from Senate Majority Leader Mitch McConnell (R-Ky.) to take up a bill addressing the status of young undocumented immigrants has no counterpart of similar clout in the House. There, conservative Republicans who have long been suspicious of bipartisan immigration talks have been able to snuff out any momentum.

Another obstacle is Trump, who has swung wildly between reaching out to Democrats and sticking to hard-line demands. In a Monday statement, he made clear that he will be the ultimate judge of any deal.

“We will make a long-term deal on immigration if, and only if, it is good for our country,” he said.

Still, Democratic senators said they believe that a Senate immigration bill passing with a significant bipartisan majority would ultimately force Republicans to capitulate.

“There’s going to be an awful lot of pressure,” said Sen. Claire McCaskill (D-Mo.), one of the roughly 30 senators who worked to break the shutdown impasse. “What, are they going to start with members of the military? Are they going to deport them? Are they going to start with the teachers? Are they going to start with the college student that’s in med school? At a certain point, the American people want these young people to have protection.”

The unfolding debate stands to put intense pressure on House Speaker Paul D. Ryan (R-Wis.), who spent much of his congressional career pushing for a bipartisan immigration deal — only to see the effort suddenly crumble in 2014, when then-House Majority Leader Eric Cantor (R-Va.) lost to an immigration foe in a primary.

When Ryan pursued the speakership more than a year later, he won wide backing from Republicans after pledging to pursue only immigration legislation that had the support of a majority of GOP lawmakers.

Ryan has kept that promise while acknowledging a new foil: Trump, who campaigned for a crackdown on illegal immigration and moved last year to cancel a program, Deferred Action for Childhood Arrivals, or DACA, that protected hundreds of thousands of dreamers.

On one hand, Ryan has repeatedly pledged to bring forth a bill protecting dreamers, and brokering a compromise could help protect GOP members running in competitive races in this year’s midterm elections. On the other hand, he has said no immigration bill can pass the House without Trump’s support, and Trump has yet to back any legislation that has the bipartisan support necessary to pass both chambers.

Ryan has kept a tough line as the DACA debate has come to a head in advance of a March 6 deadline for the program’s expiration.

“We don’t want to kick kids out,” he said Monday in a Fox News Channel interview. “But . . . we don’t want to say to people in other countries, ‘Oh, get yourself to America illegally because sooner or later you will get legalized.’ We need to make sure that we control immigration.”

Later Monday, on the House floor, he struck a more conciliatory note: “We need to move forward in good faith,” he said, citing the need for action on immigration. “Let’s address these urgent challenges.”

Trump and conservative lawmakers have dismissed a proposal by Sens. Lindsey O. Graham (R-S.C.) and Richard J. Durbin (D-Ill.) that would offer legal status and an eventual path to citizenship for more than 1 million dreamers in exchange for several billion dollars of border security funding and modest changes to two immigration programs Republicans are seeking to end entirely.

House Republicans, meanwhile, are entertaining much more restrictive legislation that would grant legal status only to those who applied for and received DACA protections. In addition, the bill sponsored by Reps. Bob Goodlatte (R-Va.), Michael McCaul (R-Tex.), Martha McSally (R-Ariz.) and Labrador would reduce the number of authorized legal immigrants by roughly 25 percent — about 260,000 a year — while also authorizing border-wall construction, funding 10,000 new Border Patrol and immigration enforcement officers, and mandating employers use the federal “E-Verify” system to screen whether employees can work legally in the U.S.

The legislation also would crack down on “sanctuary cities” that do not cooperate with federal immigration authorities.

Any one of those provisions represents a deal-killer for Democrats — as well as for many Republicans. House GOP leaders have been skeptical that they can build enough support among Republicans alone, but the bill’s sponsors and House Majority Whip Steve Scalise (R-La.) have launched an effort to get more members on board in hopes of staging a vote before the March deadline.

Scalise, in an interview Monday, said the House bill is a “good start” that could become a vehicle for further compromises.

“You should let everybody get together and bring their best ideas, and you eliminate the things that can’t be part of a final product that can pass the House, and then you end up with a bill that addresses the problems,” he said. “It’s got to secure the border. You’ve got to fund the wall. You’ve got to find a solution to DACA. And President Trump has to support it. If you could achieve those things . . . that’s a bill that can pass the House.”

Bipartisan talks among House members have produced a bill sponsored by Reps. Will Hurd (R-Tex.) and Pete Aguilar (D-Calif.) that would take a much narrower approach to protecting dreamers and could ultimately get Democrats on board. But under pressure from their conservative ranks, House Republican leaders have shown little enthusiasm for the bill.

Any hopes for bridging the gap between the parties rests in the Senate, where at least nine Democrats will have to join 51 Republicans to pass a bill. Sen. Joe Manchin III (D-W.Va.) left a White House meeting with Trump on Monday convinced that the president would ultimately back an immigration deal that his fellow senators manage to craft.

“He’s very sympathetic towards the children, towards these young people,” he said. “He wants it to be done.”

But Rep. Andy Biggs (R-Ariz.), a member of the conservative House Freedom Caucus who holds hard-line immigration views, said it was folly for senators to think they could pressure the House to accept their deal.

“It shows a certain kind of legislative naivete to believe that you can guarantee what’s going to happen in the other body when you can’t even guarantee what’s going to happen in your own body,” he said.

Correction: A earlier version of this story incorrectly described the E-Verify system. The federal database checks employees’ eligibility to legally work in the U.S., not their immigration status.