Senate Republicans are in talks with the White House about a deal to amend the National Emergencies Act — a move that could lead GOP lawmakers to avoid a fight with President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE over his emergency declaration to build a wall on the Mexican border.

Sen. John Thune John Randolph ThuneSenate GOP sees early Supreme Court vote as political booster shot Romney backs pre-election Supreme Court vote, paving way for McConnell, Trump Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-S.D.) said GOP senators are discussing reining in a president’s ability to introduce future emergency declarations, an idea that has gained growing interest within the caucus in the wake of Trump’s declaration of an emergency to build a wall.

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If senators are able to get a deal this week on amending the National Emergencies Act, GOP leadership is hoping it could impact how some senators vote on the resolution of disapproval blocking Trump’s emergency declaration and potentially even resulting in it falling short of passing the Senate.

“Our members are still having conversations with the White House,” Thune said, adding that there was “quite a bit” of interest within the caucus on amending the National Emergencies Act.

Thune said the resolution of disapproval would likely pass, but that the number of GOP senators who vote for it — which some have estimated could be as many as 15 — would be low, helping Trump avoid a stinging rebuke on the Senate floor.

"I think there are some who are looking for something that would — they 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," Thune said.

Sen. Roy Blunt Roy Dean BluntSocial media platforms put muscle into National Voter Registration Day Senate GOP faces pivotal moment on pick for Supreme Court This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (Mo.), a member of GOP leadership, said the hope was that a deal would result in a different outcome on the resolution of disapproval.

“I think so. I think there’s a hope that that could happen,” he said.

A spokesman for the White House didn’t immediately respond to a question about the talks.

One proposal, spearheaded by 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) and discussed by Republicans, would require Congress to vote to continue a future emergency declaration after 30 days.

Republicans have been hunting for an exit strategy from the showdown with Trump.

The Senate is expected to vote this week on a resolution of disapproval blocking Trump’s emergency declaration. The measure is unanimously backed by the Senate Democratic Conference and four Republican senators have voiced support, giving it a majority.

Trump has promised to veto the measure, which has already been passed by the House. But Republicans would like to avoid the fight.

Sen. Thom Tilllis (N.C.), one of the four Republicans publicly supporting the resolution of disapproval, said Monday evening that he was in talks with the White House but declined to discuss the substance of his negotiations.

Asked by The Hill on Tuesday about amending the National Emergencies Act, Tillis said getting a deal would change how he votes on the resolution of disapproval.

If Tillis changes his vote and Republicans don't have any other defections, that would lead to a 50-50 tie and allow Vice President Pence to cast a vote that prevents it from passing the Senate.

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 (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 (Ky.), two of the other GOP yes votes, indicated Tuesday that a deal on amending a president's emergency powers wouldn't change how they view the current emergency declaration.

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

Roughly a dozen Republican senators remain on the fence about the House-passed resolution, raising concerns that the number of GOP "yes" votes could hit double digits, which would be an embarrassing setback for Trump.

Sen. 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.), who is undecided, said on Tuesday that there have been discussions on amending the National Emergencies Act.

“I’m listening to it. I would like to be able to support the president and my oath to the Constitution, as would many other Republicans,” he said.

Asked if a deal on amending a president’s emergency powers would impact how he voted on the resolution of disapproval he demurred.

“There are many ideas being discussed,” he said.

Updated at 1:44 p.m.