WASHINGTON -- Four senators -- two Republicans and two Democrats -- are taking a step to protect special counsel Robert Mueller's job as U.S. President Donald Trump has angrily mused about firing him.

Legislation offered on Wednesday by Republicans Thom Tillis of North Carolina and Lindsey Graham of South Carolina and Democrats Chris Coons of Delaware and Cory Booker of New Jersey would give any special counsel a 10-day window to seek expedited judicial review of a firing.

The measure, which combines two bipartisan bills introduced last summer, signals escalating concerns in Congress as Trump fumes about a Monday FBI raid of the office of his personal attorney, Michael Cohen. Trump has privately pondered firing Deputy Attorney General Rod Rosenstein, who is overseeing Mueller's investigation, and publicly criticized Mueller and his Russia inquiry.

Mueller is investigating potential ties between Russia and Trump's 2016 campaign, and examining whether the president's actions constitute obstruction of justice. As the investigation has worn on, Trump has called it a "witch hunt." On Monday, after the Cohen raid, he said it was "an attack on our country." In a tweet Wednesday, he said the investigation is "never ending and corrupt."

The raid was overseen by the U.S. attorney's office in Manhattan and was based in part on a referral from Mueller, said Cohen's lawyer, Stephen Ryan.

Graham said in a statement that the purpose of the bill is to ensure a special counsel isn't fired for political reasons.

"I think this will serve the country well," he said.

Coons said it's time for Republicans and Democrats to "stand up and make it clear that we are committed to the rule of law in this country."

After introducing similar bills in August, when Trump first began criticizing Mueller's investigation, Tillis and Graham kept quiet for months about the need for the legislation while Democrats continued to push it. The two GOP senators said they didn't think Trump would really move to fire Mueller. But the four senators -- all members of the Senate Judiciary Committee -- moved to push out a new, combined bill in the hours after Trump's tirade Monday.

Some Republicans still say they see no need for the legislation.

"I don't think it's necessary," said Texas Sen. John Cornyn, the No. 2 Republican in the Senate, said after the legislation was introduced. "And if it did pass, would the president sign it? I think it's unlikely that he would."

Senate Majority Leader Mitch McConnell, R-Ky., has similarly shown little interest, saying Tuesday he doesn't think Mueller will be fired.

Still, Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, told reporters on Wednesday the legislation could come up as soon as next week for a committee vote. He has said in the past he wanted the two bills to be reconciled before the committee could consider it.

Now that has happened, Grassley said he has "some obligation to move along with it."

On Tuesday, Grassley told the Fox Business Network that "it would be suicide for the president to want to talk about firing Mueller."

No similar legislation has moved in the House. Speaker Paul Ryan, R-Wis., made a similar comment to McConnell on Wednesday, saying he doesn't think Mueller will be fired.

"I have assurances that it's not because I've been talking to people in the White House about it," Ryan said.

The legislation would write into law existing Justice Department regulations that say a special counsel can only be fired for good cause by an senior Justice official. And the expedited review would determine whether the special counsel was fired for good cause.

As the current regulations stand, any dismissal for cause would have to be carried out by Rosenstein, who appointed Mueller in May 2017 and has repeatedly expressed support for him.

White House press secretary Sarah Huckabee Sanders appeared to challenge the existing regulations on Tuesday, telling reporters that Trump "certainly believes he has the power" to fire Mueller, though he isn't taking that step now.