Sen. John Cornyn John CornynTumultuous court battle upends fight for Senate Texas Democrats roll out first wave of planned digital ads as Election Day nears Calls grow for Biden to expand election map in final sprint MORE (R-Texas) warned on Tuesday that it would be a “big mistake” for President Trump Donald John TrumpBubba Wallace to be driver of Michael Jordan, Denny Hamlin NASCAR team Graham: GOP will confirm Trump's Supreme Court nominee before the election Southwest Airlines, unions call for six-month extension of government aid MORE to fire special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE and predicted it would not happen.

“I don't think the president's going to fire him because I think it would be a big mistake,” he told The Hill.

Pressed on the consequences, the No. 2 Senate Republican urged Trump to let Mueller continue his probe into Russia's meddling in the 2016 election and potential collusion between the Trump campaign and Moscow.

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“I don't think he or I or anybody could predict what the consequences might be, but there would be a lot of backlash, so I think he should just let Mr. Mueller do his job,” he said.

Cornyn was one of several Republicans on Tuesday who doubled down on warnings that Trump leave Mueller alone.

Sen. Chuck Grassley Charles (Chuck) Ernest GrassleyGardner signals support for taking up Supreme Court nominee this year Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee McConnell digs in on vow to fill Ginsburg's Supreme Court seat MORE (R-Iowa), chairman of the Judiciary Committee, said it would be “suicide” to fire the former FBI director. Sen. Thom Tillis Thomas (Thom) Roland TillisGrassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee Trump to include North Carolina in offshore drilling moratorium, senator says Biden's six best bets in 2016 Trump states MORE (R-N.C.), downplaying Trump’s comments, told CNN that “thematically, he has said similar things before.”

Cornyn separately told reporters that lawmakers have warned the White House that it would be a mistake to fire Mueller.

“I think it's pretty universally being conveyed,” he said.

Trump is lashing out after the FBI raided Michael Cohen's offices and hotel room reportedly off a referral from Mueller's team.

“Attorney–client privilege is dead!” Trump said in a tweet, adding: “A TOTAL WITCH HUNT!!!”

He said Monday that “many people” had said he should fire Mueller.

But doing so would cause a tremendous storm in Washington with consequences that could fall on Republicans in the midterm elections, which are taking center stage on Capitol Hill.

Republicans are increasingly worried about holding onto their House majority in an election season likely to be defined by Trump. They have a much better chance of holding the majority in the Senate, because Democrats are defending more than twice as many seats as the GOP.

Senators have introduced two bills that would limit Trump and the Justice Department's ability to fire Mueller. But GOP leadership has downplayed the need for the legislation because they don’t believe Trump will fire Mueller.