Senate Judiciary Committee Chairman Chuck Grassley Charles (Chuck) Ernest GrassleyThe Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy Read: Senate GOP's controversial Biden report MORE (R-Iowa) says acting Attorney General Matt Whitaker Matthew G WhitakerEx-federal prosecutor: 'Thank God' Whitaker is gone, Barr will bring 'integrity' back to DOJ GOP pollster says Dems are relitigating 2016 election with investigations of Trump Former senior FBI official calls Whitaker hearing ‘disgraceful’ MORE should not have to recuse himself for comments he made “as a private citizen,” but adds the question may soon “answer itself.”

Whitaker, whom President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE named last week to oversee the Justice Department following the ouster of former Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE, has made multiple remarks critical of special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE’s Russian investigation, which Democrats say disqualifies him from overseeing it.

Asked if Whitaker should step aside as the official in charge of the special counsel’s oversight, Grassley said Tuesday, “There may be reasons, but if the reason you're asking me is because as a private citizen he gave his opinion on certain things then the answer is no.”

“He was a private citizen – what's that got to do with his officials duties? But it really doesn't matter because right now, he's going to go to ethics people and ask if he's got to be recused so that's going to answer itself,” Grassley told Hill.TV in an interview.

Fellow Judiciary member Sen. Pat Leahy (D-Vt.), however, blasted Republicans for not fighting Whitaker’s appointment to be the nation’s chief law enforcement official.

“This committee is rubber-stamping anything Donald Trump wants … even when Trump says he wants judges that will do whatever he tells him to – they go along with that – I've never seen anything like that before in 40 years here,” Leahy told reporters.

Democrats question whether Whitaker’s appointment as the acting attorney general is constitutional, given that his previous position did not require Senate confirmation.

“No matter what the Trump Justice Department says, there is no acceptable justification for this appointment — and even conservative justices on the Supreme Court have essentially made that argument. Certainly, no significant actions under Whitaker's authority should be taken at the department,” said Democratic Sen. Ron Wyden Ronald (Ron) Lee WydenDemocrats call for declassifying election threats after briefing by Trump officials Read Democrats' report countering Republicans' Biden investigation Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE (Ore.).

Grassley however, believes Whitaker does have legal authority to take on the acting role.

"I asked [Whitaker] that very question when I talked to him last week on the phone and he says they checked with the [Office of Legal Counsel] and they said ‘yes' and they quoted the 2003 like appointment to the office at OMB – and it was a very similar situation – that OLC [said] was legal at that time,” he said.

Still, Democrats and at least one Republican on Capitol Hill, Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (Ariz.) want to take steps to prevent Whitaker from shutting down the Mueller investigation.

Flake and Sen. Chris Coons Christopher (Chris) Andrew CoonsMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (D-Del.), co-sponsors of the Special Counsel Independence and Integrity Act, which the Judiciary Committee approved in April, are pressing for a full Senate vote on the bill as soon as possible.

“Senator Flake and I will be doing a live unanimous consent [Wednesday] morning; Sen. Flake is talking with his caucus and his caucus leadership. It is my hope and expectation that we will find a way to get a floor vote on this bill,” Coons told reporters Tuesday.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) however, has indicated that he has no intention of allowing a stand-alone vote on the measure.

Lacking a vote, Democrats may attempt to attach the bill to a must-pass spending bill.

“There are a variety of approaches that we ought to take, certainly the spending bill is a very strong option. My bottom line is that I believe that there ought to be bipartisan support for ensuring that Bob Mueller can go forward with his work,” Wyden said.

Coons noted one drawback to using the spending bill as a vehicle: “That’s several weeks away, so it's my hope we get something done before that.”

– Molly K. Hooper