Many Democrats in Congress have insisted that immigration be a component of the temporary spending bill.
But Democrats, under the plan being developed in the House, would win an unrelated high-priority item: a six-year reauthorization of the Children's Health Insurance Program (CHIP), according to lawmakers. It was unclear whether the House Republican leadership would get enough votes to pass the measure in that chamber.
The conservative House Freedom Caucus was to meet late on Tuesday and its head, Representative Mark Meadows, told reporters he did not know if a "compelling" case had been made for another temporary spending bill that would fail to bring the big increases in defense spending his group is seeking.
Republicans were also discussing delaying three Affordable Healthcare Act taxes: two-year delays of a medical device and a "Cadillac" tax for high-end insurance plans and a one-year delay in 2019 of another health insurance tax.
Meanwhile, Senate Majority Leader Mitch McConnell warned that a government funding bill should not be held "hostage" to the immigration debate. And the White House director of legislative affairs, Marc Short, told reporters there was no artificial timeline for a deal on so-called Dreamers and that it would be "herculean" to get it done by this week.
The negotiating climate has become increasingly poisonous after a sudden halt last week in talks toward a deal to shield the Dreamers from deportation.
Trump rejected a bipartisan agreement reached by a group of senators. Divisions between Republicans and Democrats then deepened amid an uproar over Trump's reported use of the word "s___hole" when speaking about African countries last week. Trump has denied using that word.
The head of the Congressional Hispanic Caucus expressed her opposition to the bipartisan Senate deal, although she said she had not seen its text and noted it had some positive aspects.
"In its current form I'm probably a no," Representative Michelle Lujan Grisham, a Democrat, said in an interview.
The Senate approach, Lujan Grisham said, would reduce the parents of Dreamers to "second-class citizens" because they would receive temporary protections and no pathway to citizenship, as well as other problems.
Republican Senator Lindsay Graham on Tuesday blamed White House staff for altering Trump's positive view on the Senate bipartisan agreement on the Deferred Action for Childhood Arrivals (DACA) program that protects the Dreamers.
"I will say I don't think the president was well-served by his staff," Graham said.
If a temporary "continuing resolution" to keep the government operating results, it would be the fourth such measure since the 2018 federal fiscal year began on Oct. 1, a sign of Washington's serious struggles to pass spending legislation.