The new House Republicans’ stand underscored the uncertainty about immigration. Mr. Trump’s positions vacillate daily. And members of both parties are divided. Some Democrats are pressing for confrontation, while others seem to fear a political backlash. Some Republicans are searching for compromise against a conservative tide of anti-immigrant fervor.

Lorella Praeli, the director of immigration policy and campaigns at the American Civil Liberties Union, described the House legislation as a “collection of hard-line provisions designed to sabotage, rather than advance, the possibility of a bipartisan breakthrough.”

It was not clear if the proposal would ever come up for a vote in the House, especially after Tuesday’s White House meeting established the parameters for a bipartisan deal. And it is all but certain to have no future in the Senate, where immigration legislation would need 60 votes for passage and therefore could not make it through the chamber with only Republican support.

The immigration debate on Capitol Hill grew more complicated after a federal judge ruled Tuesday that, for now, the Trump administration could not end the DACA program.

The judge, Judge William Alsup of Federal District Court in San Francisco, wrote that the administration must “maintain the DACA program on a nationwide basis” while lawsuits challenging the decision to end the program move ahead.

Mr. Trump lashed out on Twitter, saying that the United States court system was “broken and unfair,” and members of both parties and immigration activists struggled to understand the legal and political implications of the judge’s ruling.

Officials at the Department of Homeland Security, which administers the program for young immigrants, said they are preparing to follow the order even as they await possible action by the Justice Department to appeal the ruling in the days ahead.