But White House officials said the president would be cautious about offering a full-throated endorsement of either of the measures that are slated for a vote next week. Mr. Trump does not relish the idea of leading the charge for a bill that might not pass, and his advisers have told him that House Republicans — even those who support the legislation itself — may be reluctant to vote for it if they believe it has no chance of passing the Senate.

The hard-line bill, known as the Goodlatte bill after its chief author, Representative Robert W. Goodlatte of Virginia, is highly unlikely to garner enough votes to pass the House. But the compromise bill also faces a highly questionable path because conservatives, having secured a vote on the Goodlatte bill, may have little incentive to vote for a more moderate measure that could be perceived as providing “amnesty” to Dreamers.



“We’re working to try to get a bill that will pass,” said Representative Carlos Curbelo, Republican of Florida and a leader of moderates who have pushed for the House to vote on immigration. “I don’t think anyone’s in a position to make any guarantees on whether a bill will pass or not.”

Immigrant rights advocates accused the immigration moderates of caving to party pressure.

“It’s a show vote for the right-wingers and a show vote for the so-called moderates,” said Frank Sharry, the executive director of America’s Voice, an immigrant rights group. “Neither will pass. They will not get Democratic support. It’s a sham. The heroic moderates who were going to fight for Dreamers turned out to be easily rolled by Ryan and the Freedom Caucus.”

The votes next week will put the politically divisive issue of immigration front and center in the national debate in the middle of a difficult election year for Republicans. It comes nine months after Mr. Trump moved to end the Deferred Action for Childhood Arrivals program, an Obama-era initiative also known as DACA, which protected Dreamers from deportation.