Democrats are pushing for 'immediate' legislation to protect the Mueller probe as rumors about Rosenstein's future swirl

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Robert Mueller.

• Democrats are pushing Congress to pass legislation protecting special counsel Robert Mueller.
• The renewed focus on such legislation comes after reports suggested that Deputy Attorney General Rod Rosenstein could soon depart his position.

Democrats are pushing for "immediate" legislation to protect special counsel Robert Mueller after a whirlwind Monday featured reports suggesting that Deputy Attorney General Rod Rosenstein could soon depart his position.

"We shouldn't wait for President Trump to further obstruct justice," Rep. Eric Swalwell, a Democrat form California, told Business Insider. "The House should have a floor vote immediately on legislation to protect the Mueller investigation."

Though Rosenstein did not resign or get fired on Monday, the White House announced that Rosenstein and President Donald Trump will meet on Thursday. Last week, The New York Times and other outlets reported that Rosenstein discussed invoking the 25th Amendment and removing Trump from office in the days the immediately followed the president firing FBI Director James Comey. Rosenstein also mentioned secretly recording Trump, The Times reported.

Rosenstein disputed the account, saying it was inaccurate, adding that "there is no basis to invoke the 25th Amendment." A Justice Department spokeswoman told The Times that Rosenstein's comment about recording Trump was made sarcastically.

Democrats, responding to news of Rosenstein's possible departure, pushed for legislation that had been passed by the Senate Judiciary Committee with Republican support earlier this year but was never brought forth before the full body for a vote.

In April, the committee approved legislation that would protect Mueller from being fired by giving him and other special counsels the ability to challenge such a firing in court. After the Rosenstein rumors heated up on Monday, Democratic House and Senate aides told Business Insider that Democrats will push for legislation ensuring Mueller can only be fired for good cause and that any such firing is subject to judicial review.

The April legislation passed by the Senate Judiciary Committee would do that, but Senate Majority Leader Mitch McConnell - who at the time did not think Trump would consider firing Mueller - promised not to put it on the floor. Meanwhile, House Republicans and Trump are unlikely to vote for and sign such legislation.

Additionally, some Republicans expressed concern that legislation aimed to prevent the president from firing an executive branch official would be unconstitutional.

That bill was sponsored by Democratic Sens. Chris Coons of Delaware and Cory Booker of New Jersey and Republican Sen. Thom Tillis of North Carolina and Lindsey Graham of South Carolina. Four Republicans voted in favor of the bill in April - Tillis, Graham, Senate Judiciary Chairman Chuck Grassley of Iowa, and Sen. Jeff Flake of Arizona.

Prominent Democrats - such as House Minority Leader Nancy Pelosi and Sen. Elizabeth Warren of Massachusetts - called for Congress to pass such legislation.