Conway raised her objections on Twitter, where she wrote: "FEC report: Mueller's team includes big Democrat donors. The president was pleased by the ambiguity of his position on Mr. Mueller, and thinks the possibility of being fired will focus the veteran prosecutor on delivering what the president desires most: a blanket public exoneration".
But after the evidence of former Federal Bureau of Investigation director James Comey last week, Mr Gingrich said he had changed his mind.
Mueller's investigation will oversee an FBI probe into whether members of Trump's campaign team and his associates colluded to help Russian Federation with its interference in the election.
Donald Trump is in way over his head, and his presidency looks like it is living on borrowed time.
Rosenstein is charged with Mueller's fate because Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation.More news: $447.8 million Powerball jackpot winning ticket sold in Riverside county
Mueller, who preceded Comey as Federal Bureau of Investigation director, was the longest-serving director since J. Edgar Hoover. "I think he's weighing that option".
Democratic senators repeatedly criticized Sessions for dispatching Rosenstein to testify Tuesday in his place about the Justice Department's budget to an Appropriations subcommittee.
Trump told NBC's Lester Holt in an interview on May 11 days after Comey was sacked that he fired him because "this Russian Federation thing with Trump and Russian Federation is a made up story".
"I think it is a consideration the President has had, because (Robert) Mueller is illegitimate as special counsel", Ruddy told CNN's Chris Cuomo on "New Day" Tuesday.
Later in the hearing, Shaheen brought up reports that Trump may try to force the removal of Robert Mueller, the special counsel now heading up the Russian Federation probe.More news: Rory McIlroy calls out Steve Elkington after 'bored' remark
The White House forcefully disputed Ruddy's claims, saying he speaks for himself, not the president. I think it's pretty clear by what one of his lawyers said on television recently.
NPR reported on Friday that Mueller was being considered to lead the Federal Bureau of Investigation before being named special counsel.
Sen. Susan Collins (R-Maine) followed up, asking Rosenstein whether he'd spoken to Trump about the appointment of Mueller or discussed Mueller with the president in any way. The Attorney General may remove a Special Counsel for misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of Departmental policies. If you thought the crowd numbers at the major anti-Trump rallies have been large, just wait and see what happens if Trump fires Mueller.
The check against Trump firing Mueller is less legal than political. I do have questions for the attorney general.
Rep. Adam Schiff, a California Democrat, says such a move would "be the last straw" for many in Congress and would have "echoes of Watergate", when President Richard Nixon dismissed special prosecutor Archibald Cox over Cox's subpoenas for White House tapes.More news: Donald Trump is under pressure and it doesn't look good
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