Senate Republicans have only 24 hours left to come up with a solution to stop a Democratic-backed resolution that chastises President Trump.

The Senate is slated to vote on the disapproval resolution Thursday, and four Republicans have said they will join all 47 Democrats to pass the measure blocking Trump's emergency declaration to build a wall along the U.S.-Mexico border.

Republicans are scrambling to iron out their strategy, hunting for an eleventh-hour escape hatch as they near a showdown with Trump, who has threatened to issue his first veto if the resolution of disapproval reaches his desk.

Sen. Rand Paul (R-Ky.) predicted that votes in support of the measure could reach the high 50s, despite pressure from the White House.

"They're being beaten up right now. So, if you see anybody that's got blood dripping out of their ear, they may be changing. There's still a significant number, but there's a lot of people being bruised," Paul said about his GOP colleagues.

The White House is stepping up its efforts to sway the dozen GOP senators publicly on the fence and potentially flip the four detractors. Trump urged the caucus to "get tough" on border security, highlighting intraparty tensions on the issue, and Vice President Pence met with a handful of undecided senators Tuesday.

Senate Majority Leader Mitch McConnell (R-Ky.) said a vote on the resolution of disapproval will take place Thursday and Republicans would go down to the wire as they mull their floor strategy.

"It is no secret that the use of the national emergency law has generated a good deal of discussion, and we'll continue having those discussions, but it will all come to a head on Thursday," McConnell told reporters during a weekly press conference.

Senators emerged from a closed-door lunch saying their discussions on strategy were ongoing as Trump's emergency declaration has dominated weeks of private caucus meetings, injecting late-game uncertainty into the Senate's schedule.

"Both with respect to substance and process, no final decisions have been made, so we'll see," said Sen. John Thune (S.D.), the No. 2 Republican senator. "You've got a short window here for something to come together."

"They want us to vote against the resolution of disapproval," added Sen. John Cornyn (R-Texas) when asked what the White House was requesting. "Some people want to express themselves in different ways."

A handful of Republicans have been trying to come up with a plan to either amend the House-passed resolution or craft an alternative. But with the vote just a day away, no proposal has materialized.

Senators are also locked in discussions with the White House about separate changes to the National Emergencies Act, the 1976 law Trump invoked to declare his national emergency. Pence met with Republican Sens. Rob Portman (Ohio), Pat Toomey (Pa.), Thom Tillis (N.C.), Lamar Alexander (Tenn.) and Mike Lee (Utah) on Tuesday ahead of a GOP lunch.

Tillis described the talks as a "work in progress" but said after the meeting that if they could reach an agreement on revising the National Emergencies Act, he would change how he votes on the resolution of disapproval. He is one of four Republicans who are expected to vote in favor of the measure.

If Tillis flips his vote and Republicans are able to prevent any other potential defections, that would result in a 50-vote tie, allowing Pence to reject the resolution of disapproval.

Republicans are eager to sidestep a showdown with Trump, who remains popular among the party's base. For weeks they have grappled with how to avoid breaking with the president on border security while also voicing their concerns about the precedent being set with an emergency declaration that could help a future Democratic president force through proposals on issues such as gun control or climate change.

But the White House has an uphill climb if it wants to derail the resolution of disapproval. Members of Republican leadership on Capitol Hill appeared skeptical that even getting a deal to rein in Trump's emergency powers could pave the way for defeating the resolution of disapproval, suggesting instead it would just minimize additional GOP defections.

"I think there's probably still enough members" that it would pass, said Thune, asked if a deal on amending Trump's emergency powers could result in the resolution failing in the Senate.

"I think there are some who ... would feel comfortable in the end voting against the resolution as long as they had something they could point to that actually is modernizing the underlying statue," he added.

Sen. Roy Blunt (R-Mo.) hesitated when asked if he thought a deal could spike the resolution of disapproval, but said he thinks it would help drive down the number of Republicans who break with Trump.

"I think the two things that would be important would be the president indicating his support of that or something like it ... and the leader committing that this would be something that would be on the floor," he said.

In addition to Tillis and Paul, Sens. Susan Collins (R-Maine) and Lisa Murkowski (R-Alaska) have said they will support the House-passed resolution of disapproval. Collins and Paul said Tuesday that they were open to changes to the National Emergencies Act but viewed it as a separate issue because it would only apply to future national emergencies.

"The issue before us isn't affected by amending the law in the future, so it does not change my views," Collins said.

In addition to the four declared "yes" votes, roughly a dozen senators have yet to say how they will vote on the measure.

Lee on Tuesday introduced legislation that would rein in a president's ability to issue future emergency declarations by requiring Congress to pass a resolution approving such a declaration within 30 days.

He voiced concerns about the constitutional issues sparked by Trump's emergency declaration during a lengthy, rare hallway interview with reporters, but declined to say how he would vote on the resolution of disapproval.

"The time will come when we will be saying what we're going to do," he said. "In the meantime, there are other considerations here."