Congressional Republicans struggled Monday to find a way to persuade President Trump to back off a public threat to shut down the government over border wall money, staying largely in the dark over the impasse that could halt pay for hundreds of thousands of federal workers by the end of the week.

At the White House, Trump has remained disinclined to support even stopgap measures that would keep federal government operations running for a week or two, told by his closest advisers that he would have even less leverage when Democrats take control of the House next month. Trump is also bolstered by support of rank-and-file Border Patrol agents, whose union leader told the president in a recent Oval Office conversation that they would back a wall-induced shutdown if it came to that point.

All that has left Republican lawmakers who are eager avoid a shutdown unsure whether Trump would ultimately come around to at least one option that would end the impasse before Friday. Without a resolution that the president could sign before midnight Friday, about 800,000 federal workers will be furloughed or be forced to work without pay in a partial shutdown that Trump has already - and proudly - claimed as his own.

"How are we going to get out of it? Well I think that should factor into people's calculations," said Senate Majority Whip John Cornyn, R-Texas, who has been publicly critical of Trump's decision to embrace shutdown tactics. "Because it's not going to get any better in January."

After a meeting of Senate Republican leaders Monday evening, Cornyn said that "if there is" a plan to avoid a shutdown, "I'm not aware of it."

Trump has told people around him that he is frustrated he does not have much leverage in the fight, and two presidential advisers said a shutdown was unlikely because there was no way the president could win. The current White House plan is to not shut down the government, both of these people said.

"He's not going to get $5 billion for the wall," one of these people said. "They can say on TV all they want that it's going to happen, but it's not going to happen."

The White House's legislative affairs team has devised a plan to keep the government open, two of the people said, even as administration officials such as senior adviser Stephen Miller are touting a hard-line position on immigration and threatening a shutdown on television.

House Republicans last week considered putting legislation on the floor that would offer $5 billion for a border wall as Trump has demanded. But Hill leadership eventually told the president that there were not enough votes to pass it, as two top Democrats had already told Trump in a remarkable Oval Office encounter last week.

Confident that they will skirt blame for any government shutdown, Democrats have become more hardened in their resolve to deny Trump the additional border security money that he called for in a string of weekend tweets. No substantive discussion has occurred between Democrats and Trump since last week's Oval Office meeting with House Minority Leader Nancy Pelosi, D-Calif., and Senate Minority Leader Charles Schumer, D-N.Y., although their respective staffs have continued to talk.

Pelosi, who is poised to take over the House speakership in about two weeks, and Schumer have offered the White House two options that they say can pass Congress: funding the one-quarter of the government at risk of a shutdown at current spending levels through the end of the fiscal year, or full funding for all the relevant federal agencies except the Department of Homeland Security, which would operate on a one-year "continuing resolution."

"His temper tantrum will get him a shutdown," Schumer said Monday. "But it will not get him the wall."

As the impasse continues, House Democrats have started drafting legislation to continue federal funding in the new year, when they officially take control, whether to reopen the government in the case of a shutdown or continue operations if the federal workforce was running on a short-term bill.

A shutdown after Friday would halt funding for the departments of Homeland Security, State, Treasury, Justice, Interior, Agriculture, Housing and Urban Development, and Commerce. Of the roughly 800,000 federal workers who would be affected, about 40 percent would be furloughed, while the rest are deemed essential and would have to report to work without pay.

"I don't think most people would see it or feel it," Cornyn said. "But it would eliminate certain critical functions at the Department of Homeland Security and elsewhere, which would hurt public safety."

Elsewhere, Trump is getting strong support for his confrontational tactics. In an interview Monday, Brandon Judd, the president of the National Border Patrol Council, said he and other officials from his union told Trump in a White House meeting last month that if Trump were prompted to shut down the government in a border wall standoff, the agents would stand behind him.

"We would support the president 100 percent if he were to force the government to shut down over wall funding," Judd said Monday. "We absolutely, 100 percent, know the importance of the wall."

Although Trump wasn't declarative about a shutdown in that Nov. 19 meeting, Judd recalled that Trump "appreciated" the input from the union, which represents about 15,000 Border Patrol agents, who could be forced to work without pay during a shutdown.

Senior Senate Republicans met in a series of meetings Monday in the office of Majority Leader Mitch McConnell but had very little insight as to what Trump would actually do - or sign.

Asked what kind of spending bill Trump would support, Senate Appropriations Committee Chairman Richard Shelby, R-Ala., responded: "We don't know that."

A Monday evening meeting with McConnell and the senator from Kentucky's top deputies also yielded little, with senior Republicans unaware of where exactly the White House stands. During the meeting, McConnell told other GOP senators that he had no information, and - referring to the White House - said "we're waiting for them," according to a senator in attendance.

"What Republicans don't want to see is us being blamed," said the senator, who requested anonymity to discuss a closed-door meeting. For his part, McConnell, in a floor speech Monday, backed a "substantial investment in the integrity of our border" while also urging a "bipartisan agreement" to ensure government operations remain open beyond Friday.

Any substantive movement on government funding legislation seemed unlikely until at least Wednesday, when House lawmakers return to Washington. The Senate has no plans to take up a government spending measure before the House does, and pressure may begin to build on lawmakers and Trump only as Washington nears the Friday shutdown deadline.

"No Senate Republican wants to see a shutdown," Sen. John Thune, R-S.D., the incoming Republican whip, said Monday evening. "Discussions are preliminary and premature, but there's - obviously, we have no intention of having a government shutdown."

The Washington Post’s Karoun Demirjian contributed to this report.