Vice President Pence is discussing an offer with Republican senators that could lead to the defeat of a Democratic resolution overturning Preside nt Trump ’s emergency declaration to build a wall on the Mexican border, according to GOP sources briefed on the matter.

Under the deal discussed between Pence and GOP senators, Trump would sign legislation reining in his power to declare future national emergencies if they defeat the resolution of disapproval.

Killing the resolution on the Republican-controlled Senate floor would spare the president a major embarrassment and avoid him having to issue the first veto of his presidency.

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But there is some skepticism among GOP senators whether Trump will actually go through with it. And the plan is hurt by the fact that a bill to curb the president’s power to declare national emergencies won’t come to the Senate floor until after the March recess.

Pence met Tuesday with a group of Republicans, including Sen. Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Utah), the sponsor of legislation to curb the president’s national emergency declaration power, as well as Sens. Thom Tillis Thomas (Thom) Roland TillisThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting OVERNIGHT ENERGY: EPA head questions connection of climate change to natural disasters | Pebble Mine executives eye future expansion in recorded conversations | EPA questions science linking widely used pesticide to brain damage in children Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (R-N.C.), Pat Toomey Patrick (Pat) Joseph ToomeyAppeals court rules NSA's bulk phone data collection illegal Dunford withdraws from consideration to chair coronavirus oversight panel GOP senators push for quick, partial reopening of economy MORE (R-Pa.), Rob Portman Robert (Rob) Jones PortmanMcConnell locks down key GOP votes in Supreme Court fight Romney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery MORE (R-Ohio) and Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP has votes to confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Tenn.). Lee’s measure would require Congress to vote to extend a national emergency declaration after a period of 30 days.

Senate Republicans familiar with the offer say there would have to be an ironclad promise from Trump to sign Lee’s bill in order to flip Republicans who currently say they will vote for the resolution of disapproval.

So far, Trump himself hasn’t made any such pledges, leaving the process in limbo.

Pence made “no commitment,” according to a White House official familiar with the meeting, and only said he would relay the possible deal to Trump.

The vice president said he would be “happy to bring their concerns to the president but made zero commitments,” according to the White House official.

The White House official noted that Tillis requested the meeting and Pence was happy to attend, emphasizing that the senators “pitched the VP a proposal” and that “he listened and said he’d take it to POTUS.”

The vice president “encouraged the senators to vote against the disapproval resolution and indicated a vote for it would be vote against securing our borders,” the source added.

A lunchtime meeting of the Senate Republican Conference on Tuesday failed to settle the internal debate over the emergency declaration and the resolution of disapproval.

“It was our usual circular conversation,” said one GOP senator. “Everyone goes around and throws out proposals and nothing gets resolved.

“There is no plan,” the source added.

Already Sens. Susan Collins Susan Margaret CollinsSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-Maine) and Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.), say they won’t change their minds on voting for the resolution. Sen. Lisa Murkowski Lisa Ann MurkowskiSenate GOP aims to confirm Trump court pick by Oct. 29: report Senate GOP sees early Supreme Court vote as political booster shot Pence defends Trump's 'obligation' to nominate new Supreme Court justice MORE (R-Alaska) doesn’t seem inclined to reverse herself, either.

“No, I think Congress should allocate the money and that’s a very strong belief. It’s also in the Constitution,” Paul said when asked whether he might alter course and vote against the disapproval resolution.

Tillis, who is up for reelection in 2020 and could face a primary challenger, however, might change his mind if Trump gives a strong enough assurance that he would support future reform of the National Emergencies Act of 1976.

Tillis told colleagues at lunch Tuesday that he thought Trump was within his power to declare a national emergency to obtain $3.6 billion in additional funding for border barriers, even though he disagrees with the use of that power.

But there are at least a half-dozen other Republicans who are considered strong possibilities to vote for the disapproval legislation, such as Sens. Marco Rubio Marco Antonio RubioOvernight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers Democrats step up hardball tactics as Supreme Court fight heats up Press: Notorious RBG vs Notorious GOP MORE (R-Fla.) and Mitt Romney Willard (Mitt) Mitt RomneySenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-Utah), who say they have already decided how they’re going to vote but haven’t yet announced it.

Other potential defectors include Portman, Toomey, Alexander and Sens. Johnny Isakson Johnny IsaksonLoeffler paints herself as 'more conservative than Attila the Hun' in new campaign ad Georgia GOP Senate candidates cite abortion in pushing Ginsburg replacement Loeffler: Trump 'has every right' to fill Ginsburg vacancy before election MORE (R-Ga.), Jerry Moran Gerald (Jerry) MoranLobbying world This World Suicide Prevention Day, let's recommit to protecting the lives of our veterans Hillicon Valley: Zuckerberg acknowledges failure to take down Kenosha military group despite warnings | Election officials push back against concerns over mail-in voting, drop boxes MORE (R-Kan.) and Todd Young Todd Christopher YoungSenate GOP eyes early exit Why the US should rely more on strategy, not sanctions Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Ind.).

Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.), who plans to vote against the disapproval resolution, predicted that it will get between 50 and 60 votes — enough to pass with the simple majority it needs.

“It will probably get over 50 but less than 60, I think,” he said.

Republicans control 53 seats, so the disapproval resolution will pass if four or more Republicans vote for it. All Democrats are expected to support it.

Paul, who has announced his support for the resolution, said the White House and GOP leaders are stepping up their pressure effort to keep Republicans in line.

“They’re being beaten upright, so if you see anybody that’s got blood dripping out of their ear, they may be changing,” Paul joked.

He said there is still “a significant number” of Republicans willing to vote for the disapproval resolution but added “there are a lot of people being bruised and beleaguered. We’ll see.”

As of Tuesday afternoon, the only vote expected on Thursday is on the Democratic disapproval resolution.

“Right now, that’s the only thing that’s going to be voted on,” said Sen. Shelley Moore Capito Shelley Wellons Moore CapitoCongress must finish work on popular conservation bill before time runs out Second GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure MORE (R-W.Va.) after meeting with colleagues over lunch to discuss the path forward.

Lee acknowledged that he won't be able to get his bill to the floor before the March recess, which is scheduled to begin Friday.

That means any plan to trade votes on Thursday's resolution would have to wait at least for a couple of weeks.

Efforts to come up with an alternative Republican resolution that would state support for the president’s efforts to secure the border while expressing disapproval of Trump’s emergency declaration have failed to yield a concrete proposal.

Toomey, who is working on a GOP alternative resolution, however, is still working with colleagues to come up with something.

Updated at 5:16 p.m.