Republicans are digging in for a long fight over reining in the president's emergency powers, setting up a potential clash with both the White House and Democrats.

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 on Friday vetoed Congress’s attempt to block his national emergency on the U.S.-Mexico border wall. With neither chamber expected to have the votes to override his veto, the president is poised to win round one of his fight with lawmakers.

But Republicans are already setting their sights on making it easier to terminate future emergency declarations — setting up an intriguing round two.

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“It’s an institutional issue, it’s a congressional authorities issue. We have the power of the purse,” said Sen. 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). “Under the National Emergencies Act, there was too much latitude that was given away … and we need to pull that back some and let it be used for legitimate national security purposes.”

Sen. 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.) added that there is “unanimity” in the GOP conference about making changes to the law in the wake of the fight over Trump’s emergency declaration to construct the U.S.-Mexico border wall.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) has tapped Sen. Ron Johnson Ronald (Ron) Harold Johnson CIA found Putin 'probably directing' campaign against Biden: report This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report MORE (R-Wis.) to craft legislation in the Senate Homeland Security and Governmental Affairs Committee that could win the 60 votes needed for a bill to defeat a filibuster and ultimately pass the upper chamber.

Under the National Emergencies Act, Congress can force a vote on a resolution of disapproval if they want to try to block an emergency declaration. But a president can veto the resolution, setting up a difficult hurdle for Congress to overcome since a two-thirds majority vote in each chamber is needed to override a veto.

Even GOP senators who sided with Trump are interested in the broader issue.

“I would like to revisit the emergency powers that Congress has provided to the executive branch,” said Sen. Mike Rounds Marion (Mike) Michael RoundsSenate GOP sees early Supreme Court vote as political booster shot Chamber of Commerce endorses McSally for reelection Senate GOP eyes early exit MORE (R-S.D.), who voted with Trump. “I do think it's going to be a healthy debate to have.”

McConnell told reporters after a closed-door conference lunch that there was “a lot of discomfort with the law” among Republicans and that they were “discussing” ways it could be altered.

“If Congress has grown uneasy with this law, as many have, then we should amend it. If the 116th Congress regrets the degree of flexibility that the 94th Congress gave the executive, the 116th Congress can do something about it,” McConnell added separately during a floor speech, announcing that he had asked Johnson to look into legislation on the issue.

Roughly a third of the Republican conference, including members of leadership, is already backing legislation from 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) that would require Congress to pass a resolution approving future national emergency declarations within 30 days. Without the approval, the resolution would be terminated.

“I don’t know of any president that likes to give up power, but clearly Congress has been asleep at the switch,” said Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas), who voted with Trump but is supporting Lee’s legislation.

Sen. John Kennedy John Neely KennedyMORE (R-La.) added that “there is a lot of people, myself included, who believe that the National Emergencies Act ... needs to be reformed.”

A battle with Republicans would just aggravate Trump's existing problems with Democrats, who are suing him in court and plan subsequent votes to challenge his declaration for the wall.

A Democratic aide said the House would hold a vote to override Trump’s veto on March 26; meanwhile, Senate Minority Leader Charles Schumer Chuck SchumerSenate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' Jacobin editor: Primarying Schumer would force him to fight Trump's SCOTUS nominee MORE (D-N.Y.) said Democrats would force a vote on blocking Trump’s national emergency every six months.

“We've got to be real careful and whether it's legislatively or in court, fight him every step of the way,” Schumer said.

Trump, as part of a failed eleventh-hour plea to get Republicans to vote against the resolution of disapproval, signaled that he could support making future changes to the National Emergencies Act, despite refusing to accept a deal earlier in the week.

Johnson, asked about Trump’s penchant for changing his mind on the issue, stressed that he would seek input from the White House.

“We’re going to need him because we want the administration to be taking a look at any exemptions that we might need to take a look at when we reclaim that authority,” Johnson said.

He added that he thought the “basic concept” of Lee’s bill was “correct” and could “pass constitutional muster” but that he expected others would have ideas on what the final legislation should look like.

“There’s a lot more complexity to this,” he said. “We’ll have a lot of input.”

An aide confirmed that Sen. 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.) is working on legislation that could draw support from Democrats, who have been skeptical of the Lee bill.

House Speaker Nancy Pelosi Nancy PelosiPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare House lawmakers reach deal to avert shutdown Centrist Democrats 'strongly considering' discharge petition on GOP PPP bill MORE (D-Calif.) and Schumer both said their party would not back the Utah Republican’s bill.

But Schumer appeared to soften his stance slightly after Thursday’s Senate vote approving the resolution against Trump, saying he wanted to look at its details. Drew Hammill, a spokesman for Pelosi, also didn’t rule out legislation on Friday, saying, “House Committees are reviewing the President’s unlawful use of the National Emergencies Act.”

Sen. Dick Durbin Richard (Dick) Joseph DurbinTumultuous court battle upends fight for Senate McConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden MORE (D-Ill.), the No. 2 Senate Democrat, predicted that Democrats would be “open” to changing the underlying law as long as it was separated from the fight over whether Republicans would back the resolution of disapproval.

“It doesn’t solve our current problem,” he added, “but it addresses the dilemma we face.”

Cristina Marcos contributed.