(CNN) Congressional Republicans downplayed the involvement of President Donald Trump and Attorney General William Barr in the sentencing of Trump's longtime confidant Roger Stone , saying they see no reason for the investigations that Democrats are demanding.

The mostly muted reaction from Republicans to the Justice Department's move undercutting career prosecutors ' recommended sentence for Stone of up to nine years -- which prompted all four prosecutors to withdraw from the case Tuesday -- fueled concerns from the President's critics that he's been emboldened in the aftermath of impeachment.

Senate Judiciary Chairman Lindsey Graham, a close ally of the President, brushed off the calls for his committee to hold hearings on the Stone sentencing, saying he didn't know why the four prosecutors had even stepped down.

"I'm not losing any sleep over them stepping down. If they're pushing for seven-to-nine-a year sentence, in this case. I think that's ridiculous," Graham said, pointing to a letter from a witness in the Stone case, Randy Credico, saying he didn't feel like Stone intimidated him.

Graham said he did not see any actions from the Justice Department that he needed to look into, though he added that the President "shouldn't be tweeting about an ongoing case. I've told him that."

"If I thought he'd done something that'd change the outcome inappropriately, I'd be the first to say," he said.

Trump's involvement in the Stone case is one of multiple actions he's taken decried by his critics since he was acquitted in the Senate's impeachment trial last week, including the firing of two witnesses who testified in the impeachment inquiry and the withdrawal of the nomination of a Treasury nominee who led the US Attorney's office in Washington when it prosecuted Stone.

"He's gotten so much worse since impeachment," said Sen. Sherrod Brown, an Ohio Democrat. "This retribution tour where he attacks, and attacks, and attacks -- I heard all kinds of Republican senators say, 'Well, he's going to get better.' Well, no sign of that at all and there won't be."

House Democrats are vowing to look into the Stone sentencing, but they have routinely faced resistance in their efforts to investigate the Justice Department since taking control of the House last year. Senate Minority Leader Chuck Schumer and other Democrats have called for the Justice Department inspector general to probe the matter, too, and Democratic Sen. Richard Blumenthal of Connecticut called on Barr to step down.

"Attorney General William Barr ought to be ashamed and embarrassed and resign as a result of this action: Directly interfering in the independent prosecution of Roger Stone," Blumenthal said.

Trump said Tuesday he did not ask the Justice Department to change the Stone sentencing, but added he had the "absolute right" to do so. Trump has tweeted multiple times about the Stone case since the initial sentencing recommendation was filed on Monday night, attacking both the prosecutors who withdrew and the judge who will ultimately hand down Stone's sentence.

The updated sentencing recommendation from the US Attorney's office in Washington filed Tuesday did not give a specific sentencing recommendation, beyond saying it should be "far less" than the seven-to-nine years initially proposed.

"Congratulations to Attorney General Bill Barr for taking charge of a case that was totally out of control and perhaps should not have even been brought," Trump tweeted Wednesday morning.

White House spokesman Hogan Gidley said Wednesday that Trump was not involved in the sentencing recommendation for Stone, and he "did not have a conversation with the attorney general" about it.

Democrats say Trump emboldened

Democrats say it's clear that Trump has been emboldened by his acquittal in the impeachment trial last week, in which all but one found him not guilty.

"I don't think there's any question about that," said Sen. Doug Jones , an Alabama Democrat. "When you start dealing with the Department of Justice you're really truly are crossing a line."

Sen. Mitt Romney of Utah, the lone Republican to vote to convict Trump , was muted in his view about the Stone case, saying if there's "any indication" that the Justice Department is not independent of politics -- that "would obviously be a real problem."

Romney said he doesn't think a Republican investigation into the matter would "change a lot."

Some Republicans were critical of the President's involvement. Sen. John Thune, the second-ranking member of the Senate GOP leadership, said Wednesday it would be best for the President not to meddle in matters at the Justice Department, such as the sentencing recommendations of Stone.

"My view is that these legal proceedings are best left to the system of justice in this country to be resolved. And I would hope in the end that that will happen," Thune said in response to questions about the controversy.

He also said it was "unfortunate people resigned," and that "you want to let the legal process move forward the way it was intended to."

Trump's actions have put several moderate senators who voted to acquit the President in a difficult spot, as they had said Trump's dealings with Ukraine were inappropriate, even if they weren't impeachable -- and they hoped Trump would learn a lesson from the impeachment process.

Sen. Susan Collins, a Maine Republican, said that she hoped he would learn to be more careful in conversations with foreign leaders -- and argued her vote to acquit the President was solely based on whether the House case had met the bar for removing the him from office.

"My vote to acquit the President was not based on predicting his future behavior. It was based solely on the issue, whether or not the House managers reached the high bar for removing a duly elected president," Collins said. "And in my judgment, they did not. That was the basis for my vote."

Asked about the Stone sentencing, Collins said: "The President should not have gotten involved."

Sen. Lisa Murkowski of Alaska, another moderate Republican, also criticized Trump and the Justice Department for intervening.

"I don't like this chain of events," she said. "The President weighs in, all of a sudden, Justice comes back and says, 'Change the deal.' I think most people in America would look at that and say, 'Hm, that just doesn't look right.' And I think they're right."

'The President has First Amendment rights, too'

But numerous other Republican senators downplayed the significance of Trump's actions, and said they saw no need for an investigation.

"I think the judge is going to take care of all that and nobody is going to question the judge's decision," said Sen. Chuck Grassley of Iowa, a former Judiciary Committee chairman.

"The President has First Amendment rights, too," said Texas GOP Sen. John Cornyn.

Sen. John Kennedy, a Louisiana Republican, said Trump's tweet was "problematic" but that he has seen "no evidence" that Trump improperly interfered.

"Schumer's always going to call for emergency hearings. Chuck's like a teenager, he's mad at everybody, especially the President," Kennedy said. "I don't see anything to investigate unless you have facts that I don't."

Democrats say they will push for investigations. In addition to calling on the inspector general to probe the matter, Schumer on Wednesday called for an emergency Judiciary Committee hearing.

"The President is claiming that rigging the rules is perfectly legitimate -- he claims an 'absolute right' to order the Justice Department to do anything he wants," Schumer said. "And the President has as his attorney general an enabler -- and that's a kind word -- who actually supports this view."

House Judiciary Chairman Jerry Nadler tweeted that he would "get to the bottom of this," while House Speaker Nancy Pelosi said: "Stepping down of prosecutors should be commended & actions of DOJ should be investigated."