Senate Republicans, including some of President Trump’s sharpest GOP critics, are rebuffing Democratic demands to pass legislation protecting special counsel Robert Mueller as his investigation into the 2016 presidential election ramps up.

"I can't imagine any administration taking a move like that," Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.) told reporters Monday when asked if legislation to shield Mueller from a potential firing was necessary.

Mueller on Monday unveiled charges against Paul Manafort, Trump's former campaign chairman, and his business associate Richard Gates. Former Trump campaign aide George Papadopoulos has also pleaded guilty to making false statements to FBI investigators.

The charges, as well as growing pressure from conservatives for Mueller to resign, sparked a new push from Democrats for Congress to pass legislation that would block the Trump administration from being able to fire the special counsel unilaterally.

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But Republicans argue the legislation isn't needed for now, because they don't believe Trump would fire or try to have the Department of Justice fire Mueller, who is widely respected in Washington.

"There's no indication that he's going to ... fire [Mueller] or pardon [anyone] at this point," said 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.), who, like Corker, has feuded openly with Trump and is not seeking reelection in 2018.

Pressed if that means he doesn't think legislation is necessary, Flake added: "We'll see."

Sen. Lindsey Graham Lindsey Olin GrahamGraham: GOP will confirm Trump's Supreme Court nominee before the election Fox's Napolitano: Supreme Court confirmation hearings will be 'World War III of political battles' Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee MORE (R-S.C.) also downplayed the chances that Mueller would get fired, saying no one in their "right mind" would fire the special counsel.

"I don’t feel an urgent need to pass that law until you show me that Mr. Mueller is in jeopardy," he told reporters on Monday evening.

Senators have offered two bills that would get the court system involved with any attempt by the Justice Department to fire Mueller.

One proposed bill, from Graham and Democratic Sen. Cory Booker Cory Anthony BookerBipartisan praise pours in after Ginsburg's death DHS opens probe into allegations at Georgia ICE facility Democratic lawmakers call for an investigation into allegations of medical neglect at Georgia ICE facility MORE (N.J.), would require a judge to approve a Justice Department request to fire Mueller or any other special counsel.

A second bill, from GOP 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 (N.C.) and Democratic Sen. Christopher Coons Christopher (Chris) Andrew CoonsMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (Del.), would let Mueller or any special counsel challenge their firing in court.

Democrats, because they are in the minority, will need the support of at least a dozen Republicans to round up the 60 votes needed to get a bill through the Senate.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) has yet to weigh in on Monday's developments. But Senate Majority Whip 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), asked if additional legislation is needed, sidestepped.

"I think [Mueller] knows what to do and he's doing it," he told reporters.

Sen. John Kennedy John Neely KennedyMORE (R-La.) told Fox News that he didn't believe legislation was "necessary."

The president previously flirted with firing Mueller, sparking bipartisan concern in Washington.

White House press secretary Sarah Huckabee Sanders said on Monday that Trump wasn't weighing firing Mueller in the wake of Monday's charges.

"There is no intention or plan to make any changes in regards to the special counsel," she told reporters.

But both CNN and The Washington Post reported that Trump grew frustrated on Monday as he watched TV coverage of both the indictments against Manafort and Papadopoulos's guilty plea, with one Republican describing the president as "seething."

Mueller is investigating Russia's election interference and potential ties between Moscow and the Trump campaign. He was appointed as special counsel by Deputy Attorney General Rod Rosenstein after then-FBI Director James Comey's firing.

Corker argued on Monday evening that Trump wouldn't repeat his previous mistake of roiling Washington as he did with Comey's firing

"He did [fire Comey] but probably wishes he didn't," Corker said. "And I just can't imagine that happening again."