Washington (CNN) As President Donald Trump rants anew about the Russia investigation, a bipartisan group of senators is trying to jump-start legislation to protect special counsel Robert Mueller from being fired.

Debate around the latest proposal offers a reminder of how much power Trump, as chief executive, holds as the Russia investigation related to the 2016 election may be closing in on him.

Still, it is not unchecked power.

The Supreme Court has long permitted Congress to put some limits on a president's authority to dismiss executive branch officials. Yet the justices have tread a fine -- and not always consistent -- line in balancing a president's removal power with protections imposed by Congress.

The crux of the current dilemma is how much Congress can limit Trump as he might order the firing of Mueller who is, within the terms of the Constitution, an "inferior" officer, that is an executive branch employee not subject to Senate confirmation and reporting to a superior officer.

The new legislation offered Wednesday would allow judicial review of Mueller's dismissal or that of any special counsel, to ensure it was for "good cause."

Some law professors, such as University of Virginia's John Duffy, say the proposal conflicts with the principle that the Constitution vests all executive power in the president "not just some fraction of it." Duffy said the framers of the Constitution believed impeachment the sole remedy for any presidential wrongdoing.

But New York University's Richard Pildes argues that cases going back a century have permitted modest limits, including judicial review, on the executive's removal power. The question Congress is properly asking, Pildes says, is: "How do you ensure a sufficiently impartial, credible investigation of the President and his top aides?"

Mueller has been investigating connections between the Trump campaign and Russian meddling in the 2016 presidential election. Trump has many times deemed Mueller's work "a witch hunt" and early Thursday said that if he had been inclined to get rid of Mueller, he would have done it already.

"If I wanted to fire Robert Mueller in December, as reported by the Failing New York Times, I would have fired him. Just more Fake News from a biased newspaper," he tweeted, trying to counter a New York Times story that said he wanted to fire Mueller in December after Mueller apparently sought Trump-related financial records. Trump's ire toward Mueller appeared to intensify this week as FBI agents raided the office and hotel room of Michael Cohen, the President's personal lawyer. Acting on a Mueller referral, agents were seeking information related to possible payments made to silence women about alleged affairs with Trump before he became President.

If I wanted to fire Robert Mueller in December, as reported by the Failing New York Times, I would have fired him. Just more Fake News from a biased newspaper! — Donald J. Trump (@realDonaldTrump) April 12, 2018

The new legislation was offered by Republican Sens. Lindsey Graham of South Carolina and Thom Tillis of North Carolina and Democrats Chris Coons of Delaware and Cory Booker of New Jersey. It would cement into law a Justice Department regulation dictating that a special counsel can be removed by the attorney general "only for misconduct, dereliction of duty, incapacity, conflict of interest, or other good cause."

Their bill would provide a 10-day window for Mueller or any special counsel to obtain judicial review to determine whether the firing was justified. If not, he would keep the job. While a challenge is pending, the legislation dictates, the special counsel's staff, documents and other materials would be preserved.

Line of succession

Right now, Deputy Attorney General Rod Rosenstein, who appointed Mueller, has authority over him. (Attorney General Jeff Sessions recused himself from the investigation related to the 2016 campaign.) If Trump were to sack Rosenstein, the deputy's successor would take control over the special counsel and scope of his investigation.

Senate Judiciary Committee Chairman Charles Grassley has declared that it would be "suicide" for Trump to order Muller to be fired, but has also questioned the need for -- and constitutionality -- of measures to protect Mueller.

Grassley said on Thursday that he would offer an amendment to the pending bill to require the attorney general to provide a detailed report to Congress "justifying significant decisions involving the special counsel, including the firing of the special counsel."

Sen. Dianne Feinstein, the top Democrat on the Judiciary panel, says such a broad requirement on the attorney general could "undermine the investigation" the law is meant to protect.

"It's vital that Special Counsel Mueller be allowed to continue his investigation without interference," Feinstein said in a statement late Wednesday, "and passing a bipartisan bill to ensure he can't be fired without cause is essential."

The overall goal of the new legislation is guaranteeing -- through the involvement of a three-judge panel -- that any effort to get rid of the special counsel is justified. It does not change the "good cause" standard for removal already in regulations.

Oversight of executive authority

One past Supreme Court case that the bill's backers use for support is Morrison v. Olson, a 1988 case when the justices upheld the constitutionality of a freestanding but now defunct independent counsel law. The court ruled that Congress did not infringe on executive power when it authorized a judicial panel to appoint independent prosecutors to investigate possible executive branch wrongdoing and when it dictated rules for the prosecutor's removal.

Justice Antonin Scalia was the lone dissenter, arguing that the legislation violated the separation of powers and allowed Congress to usurp executive power. In one of the most repeated lines of the case, Scalia wrote, "Frequently, an issue of this sort will come before the Court clad, so to speak, in sheep's clothing ... But this wolf comes as a wolf."

Over the past three decades, some legal scholars and justices have cast doubt on the rationale of Morrison v. Olson, which unlike in the current situation dealt with a separate federal ethics law. But the ruling has never been reversed. (Congress did not renew the freestanding independent counsel law when it expired in 1999.)

As senators announced their new legislation on Wednesday, Tillis pointed to broader safeguards beyond Mueller.

"This compromise bipartisan bill helps ensure that special counsels -- present or future -- have the independence they need to conduct fair and impartial investigations."

If the legislation makes it through Congress and earns Trump's signature -- a big political "if" -- it could face a skeptical Supreme Court.

Yale Law Professor Akhil Amar, who has warned against trying to legislate protection for Mueller, told CNN on Thursday that it is difficult to reconcile the "inferior" constitutional status of the special counsel with the "independence" envisioned in legislation that would allow him to challenge the executive's power to dismiss him.

"A truly inferior officer," Amar told the Senate Judiciary Committee last year, referring to the special counsel's constitutional status, "must have a superior officer within his own branch to whom he answers and who can ... remove him if the superior loses confidence" in him.

Proposals that would permit a special counsel to challenge removal in court, Amar argued, would strip power from "all Oval Office occupants -- and not just the one down the street today."