"There's no question ... that all the people who had sworn to support the Constitution would assure that there would be a peaceful transition of power, including the president,” Romney said.

Senate Majority Whip John Thune (R-S.D.) added that his party would not stand idly by if Trump tried to stay in office after losing: "Republicans believe in the rule of law and we believe in the Constitution. And that's what dictates our election process."

Hill Republicans argued Thursday morning that this year’s election would be no different than previous ones and reiterated that the Constitution guarantees that whoever loses must cede the presidency. But no one condemned Trump directly by name, and they declined to weigh in on whether it was appropriate for the president to suggest he won’t leave office.

"The winner of the November 3rd election will be inaugurated on January 20th," said Senate Majority Leader Mitch McConnell. "There will be an orderly transition just as there has been every four years since 1792."

When asked whether he takes the president’s threat seriously, McConnell simply referred back to his tweet and said "it pretty well sums up how I feel about it."

Hours after the GOP pushback, White House spokesperson Kayleigh McEnany said Trump "will accept the result of a free and fair election."

That McConnell and his colleagues felt compelled to respond at all was notable, given their general reluctance to address Trump’s incendiary tweets and statements. But Thursday’s responses were reminiscent of 2016, when Trump similarly declined to say he would concede the election if he loses.

Sen. Rob Portman (R-Ohio) called on both Trump and former vice president Joe Biden to “commit to abiding by the results, no matter the outcome.”

A spokesperson for Biden said Thursday he "obviously, has participated in a peaceful transition of power before" and will do so again.

GOP members of the Senate Intelligence Committee were notably mum about the president’s threat to remain in office if he loses. The panel recently concluded in a report on election interference that undermining trust in the election result “can have significant national security and electoral consequences,” including aiding foreign intelligence services.

“As we have done for over two centuries we will have a legitimate [and] fair election,” added Sen. Marco Rubio (R-Fla.), the chair of the Intelligence Committee. “It may take longer than usual to know the outcome, but it will be a valid one. And at noon on Jan 20, 2021 we will peacefully swear in the president.”

“I’m not a cable commentator,” Rubio added, declining to weigh in on whether the president’s comments were appropriate.

House GOP Conference Chair Liz Cheney (R-Wyo.), one of the few Republicans willing to publicly rebuke the president, said Thursday that transferring power “is enshrined in our Constitution and fundamental survival of our Republic” and vowed that American leaders would uphold their oath to the Constitution. Rep. Steve Stivers (R-Ohio), a former chair of the House Republicans’ campaign arm, echoed her remarks.

Trump’s comments are the latest headache for the Republican party, with the election just 40 days away. And Republicans’ response mirrors how they have often dealt with his most volatile remarks or actions — rebutting Trump or disagreeing with him, but without the harsh condemnation that could invite a Twitter attack from the president.

While Trump’s statement Wednesday is the furthest he’s gone in suggesting how he might respond to the election results, he’s repeatedly cast doubt about the results of the election by attacking the legitimacy of mail-in ballots based on unsubstantiated claims about fraud.

The president, who has previously suggested that the November election should be delayed and that the results “may never be accurately determined,” is trailing behind vice president Joe Biden in most public polling and control of the Senate is a toss-up.

Some Senate Republicans dismissed Trump's remarks as more of the same.

“He says crazy stuff," said Sen. Ben Sasse (R-Neb.), an Intelligence Committee member. "We’ve always had a peaceful transition of power. It’s not going to change."

Sen. Mike Braun (R-Ind.) said the topic is “preposterous” and no one should focus on the president’s equivocation.

“He stokes the fire sometimes,” he said. “If you took it seriously it would be alarming. And I don’t think that that's the case.”

Others, though, deflected to Hillary Clinton’s recent comments urging Biden not to concede the election if it is close.

“I would have the same concern when Hillary Clinton advised Biden not to concede the election,” said Sen. Chuck Grassley (R-Iowa). “We have a Constitution and the Constitution says when the presidency ends. You ask me just from the standpoint of what the president said: it isn’t very good advice from Hillary Clinton to advise Biden about that."

Sen. Roy Blunt (R-Mo.), an Intelligence Committee member and the chairman of the Inaugural Committee, also referred to Clinton’s comments and said of Trump: “I don’t know what he would mean by that.”

Blunt added: “It may take the court process to run its course. But there will be a peaceful transition of power.”

Senate Minority Leader Chuck Schumer chastised Senate Republicans Thursday for their response to the president, arguing "this is not a partisan issue" and that "democracy is at stake." Sen. Chris Murphy (D-Conn.) said that he was speaking to his Republican colleagues about Trump’s statement, while Speaker Nancy Pelosi told reporters that clear election results from voters would be an “antidote” to Trump’s comments.

The Senate passed a largely symbolic resolution Thursday afternoon from Sen. Joe Manchin (D-W.Va.) to reaffirm the chamber's "commitment to the orderly and peaceful transfer of power called for in the Constitution of the United States."

Trump also suggested Wednesday that the Supreme Court vacancy created by the death of Justice Ruth Bader Ginsburg needed to be filled ahead of the November election, in case the election results are disputed. Trump is expected to name his nominee Saturday and Senate Republicans are vowing to move forward swiftly with the confirmation process.

Senate Judiciary Chair Lindsey Graham (R-S.C.) said on Fox News Thursday that a successful transition of power could depend on whether there are nine Supreme Court Justices.

“I can assure you, it will be peaceful,” Graham said. “Now we may have litigation about who won the election. But the court will decide, and if the Republicans lose, we will accept that result. But we need a full court, and I think that's possible before the election."

Melanie Zanona and Quint Forgey contributed to this report.