The measure would allow any special counsel to request an expedited judicial review of any firing, which could then be overturned while preserving investigation records.
The moves come as Trump has stepped up his public and private criticism of DOJ officials and the Mueller probe, lashing out at the special counsel on Twitter and musing about firing Mueller in a meeting with military officials earlier this week, after the FBI raided the home and offices of Trump’s longtime personal attorney Michael Cohen.
A number of Republicans on the committee, including Grassley, have said they are concerned that the bill is unconstitutional, impinging on the president’s executive powers. With two Republicans co-authoring the bill, it would seem that the measure would pass out of committee easily, but there is a lot of consternation in the GOP ranks about bucking a president still popular with the base.
Neither Senate Majority Leader Mitch McConnell nor House Speaker Paul Ryan has committed to giving the bills a floor vote.
Rep. Adam Schiff, D-Calif., the top Democrat on the House Intelligence Committee, said Wednesday that he is crafting legislation that would require that the investigative reports developed by the special counsel’s team be delivered to Congress in the event that Mueller is fired.
Mueller is required to produce a report on his findings to Rosenstein at the conclusion of his investigation laying out the reasons why prosecution is warranted, or why prosecution should be declined. While Rosenstein is required to share information with the relevant congressional committees, Schiff said he is concerned about political interference from the White House at DOJ.
“We need to protect the integrity of that investigation,” he said. “I have never been more concerned than I am today of the potential of his firing Mueller, or even more perniciously in a way, Mueller's boss.”
The activity and new warnings against firing top DOJ come as Trump’s allies escalate their criticism of the Trump-nominated Rosenstein.
"I would fire Rosenstein in a New York minute; without any question," Joe diGenova, a former federal prosecutor who was in discussions to join Trump’s legal team, told ABC News’ Jonathan Karl and Rick Klein on this week’s “Powerhouse Politics” podcast.
DiGenova, who told ABC News Wednesday he had spoken to Trump in the past 24 hours, continued to blast Rosenstein in a Wednesday night appearance on Fox News’ ‘Hannity.’
“Rod Rosenstein is so incompetent, compromised and conflicted that he can no longer serve as the deputy attorney general,” he said, urging Attorney General Jeff Sessions to fire him.
“Anyone advising the President — in public or over the airwaves— to fire Bob Mueller does not have the President or the nation’s best interest at heart. Full stop,” his office tweeted Thursday.
Congressional Republicans are also clashing with Rosenstein over his handling of the Russia investigation and DOJ production of documents to Republican oversight investigations.
The California Republican appeared to dial down that threat Wednesday night, after the Justice Department allowed him and Rep. Trey Gowdy, R-S.C., to review a key FBI document related to the opening of the counterintelligence investigation into the Trump campaign and alleged ties to Russia in 2016.
A Justice official confirmed that the Republicans – along with Democrats on the committee – had received access to a redacted version of the document known as an electronic communication.
Still, other Republicans, while they may not support Nunes’ threat to impeach the embattled deputy attorney general, believe that top DOJ officials, including Attorney General Jeff Sessions, should resign.
“I think he’s one of the most decent people in Washington DC,” Rep. Chris Stewart, R-Utah, a member of the Intelligence Committee, said in an interview. “But I think it was a mistake to recuse himself.”
Rep. Mark Meadows, R-N.C., a leading House conservative and Trump confidant, blasted DOJ officials Wednesday for the pace of document production to the House Oversight and Judiciary Committees, where Republicans are reviewing the FBI’s handling of the Clinton email probe.
“He’s not giving us the documents and he’s not doing his job,” he said of Rosenstein. “And if he’s not going to do his job, he needs to go and find one that he will do.”
“The frustration with the AG and the deputy AG is probably more a focus of Congress and it probably makes the President’s dissatisfaction pale in comparison.”
Sen. John Cornyn, R-Texas, the second-ranking Senate Republican, who dined with President Trump and other GOP leaders last night at the White House, told ABC News that Mueller and the special counsel probe did not come up in the meeting.
"It would be a mistake and there would be consequences that the president would come to regret," he said.
As Trump and Republicans continue to question the agency and top law enforcement officials, Cornyn took to the Senate floor Thursday to defend the “rank-and-file” at the DOJ and FBI.
“We appreciate everything you do to protect the public safety and secure the public trust. These days it’s important that our appreciation for the bureau not get drowned out by the criticism,” he said.