Republican senators are demanding a public apology after a White House staffer joked about Sen. John McCain John Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE's (R-Ariz.) failing health, even as the administration is doubling down on its decision to handle the fallout "internally."

The growing divisions between the Senate GOP caucus and the White House comes on the eve of a closed-door Tuesday lunch between 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 and Senate Republicans.

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 (Texas), the No. 2 Senate Republican, said on Monday that an apology would be "appropriate ... from the person who said that really dumb thing."

Sen. John Kennedy John Neely KennedyMORE (R-La.) called staffer Kelly Sadler’s comments "stupid" and "a big mistake."

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"I think the administration should apologize, but I think Mrs. Sadler ... I think she should apologize publicly as well," Kennedy separately told CBS News.

During an internal meeting last week, Sadler dismissed McCain's opposition to Gina Haspel's CIA nomination by saying, "It doesn't matter, he's dying anyway."

Her leaked comments, which were first reported by The Hill on Thursday, have created a firestorm for the White House.

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.) on Monday called Sadler's remarks a "really unfortunate circumstance."

"Obviously what was said was very wrong and inappropriate. It would have been a lot easier if they had just nipped it right away and she came out and issued a public apology. ... Now it's drug on for five days," the No. 3 Senate Republican told reporters.

The White House signaled on Monday that neither they nor Sadler would be offering a public apology.

Deputy press secretary Raj Shah confirmed that Sadler called McCain's daughter, Meghan McCain, to apologize for her remarks but said the matter was being "dealt with internally."

And Trump on Twitter blasted not the insult but "the so-called leaks" coming out of the White House.

The so-called leaks coming out of the White House are a massive over exaggeration put out by the Fake News Media in order to make us look as bad as possible. With that being said, leakers are traitors and cowards, and we will find out who they are! — Donald J. Trump (@realDonaldTrump) May 14, 2018

Trump and McCain have had a rocky relationship. Trump mocked McCain during his 2016 presidential campaign for being captured during the Vietnam War. He's also repeatedly lashed out at the 81-year-old senator for voting against the GOP's ObamaCare repeal plan.

But Republican senators, as well as Democrats, have rushed to McCain's defense since late last week and gradually increased their pressure for the White House to formally issue an apology.

Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah), who issued his own apology to McCain last week after weighing in on his planned funeral arrangements, said on Monday that the White House should apologize "because if you make a mistake it's better to admit it and move on."

GOP Sens. Dan Sullivan Daniel Scott SullivanWill Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Republican Senators raise concerns over Oracle-TikTok deal MORE (Alaska) and 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 (S.C.), who is McCain's closest friend in the Senate, have also called on the White House to apologize.

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.), without mentioning the White House, praised McCain from the Senate floor, calling him a "genuine American hero" who has the "deepest respect" for his colleagues.

It's unclear if Senate Republicans will bring up Sadler's McCain comments during Tuesday's closed-door lunch with the president. Republicans had hoped the lunch would be a chance to take a victory lap on North Korea and the economy.

Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (R-Ariz.) confronted Trump during a 2016 caucus lunch over his earlier comments about McCain, who missed the meeting because of a Senate Armed Services Committee hearing.