New talk of 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 possibly pardoning himself drew pushback from Republicans on the Sunday show circuit this week.

Both congressional Republicans and the president's attorney Rudy Giuliani urged caution that a self-issued pardon could be politically problematic for Trump.

But Giuliani said the president “probably” has the power to give himself a pardon even though doing so would prove to be difficult.

“I think the political ramifications of that would be tough. Pardoning other people is one thing. Pardoning yourself is another,” Giuliani told ABC’s “This Week.”

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“Other presidents have pardoned people in circumstances like this, both in their administration and sometimes the next president, even of a different party will come along and pardon,” he continued.

On NBC's "Meet the Press," Giuliani went even further, saying that such a move "would just be unthinkable, and it would lead to probably an immediate impeachment."

The issue took the spotlight on Sunday after the revelation Saturday that Trump's legal team had sent a letter to 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 in January arguing that the president holds the power to pardon "if he so desired."

The confidential 20-page note, first obtained by The New York Times, states that the president has constitutional authority over federal probes, making it impossible for Trump to have obstructed justice and giving him the ability to end Mueller's investigation into potential ties between the Trump campaign and Russia.

“It remains our position that the President’s actions here, by virtue of his position as the chief law enforcement officer, could neither constitutionally nor legally constitute obstruction because that would amount to him obstructing himself, and that he could, if he wished, terminate the inquiry, or even exercise his power to pardon if he so desired,” the letter reads.

But Republican members of Congress during their Sunday show appearances expressed concern that a self-pardon would put the president in a compromising position.

“I think that would be a terrible move. I think people would erupt. I think even thinking about trying to fire Mueller is a bad move politically,” Rep. Will Hurd William Ballard HurdHillicon Valley: Oracle confirms deal with TikTok to be 'trusted technology provider' | QAnon spreads across globe, shadowing COVID-19 | VA hit by data breach impacting 46,000 veterans House approves bill to secure internet-connected federal devices against cyber threats House Democrats' campaign arm reserves .6M in ads in competitive districts MORE (R-Texas), a member of the House Intelligence Committee, told CBS’s “Face the Nation."

“So I hope we don’t have to get to that point. And it’s hard to predict what would happen, but that would create outrage on both sides of the political aisle.”

House Majority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy threatens motion to oust Pelosi if she moves forward with impeachment Kate Schroder in Ohio among Democratic challengers squelching GOP hopes for the House McCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother MORE (R-Calif.) echoed Hurd's concerns, but suggested that a self-pardon isn't necessarily on Trump's agenda.

“The president is not saying he is going to pardon himself,” McCarthy told CNN’s “State of the Union.”

“I don't know why we're walking through hypotheticals here in this process. The president has never said he would pardon himself. I don't know where the president would go forward pardoning himself, but I don't think a president should pardon themselves,” McCarthy added.

On ABC News Sunday, Giuliani affirmed that the president “has no intention of pardoning himself.”

According to a March report from the Times, a former Trump lawyer had suggested pardons for former national security adviser Michael Flynn and former Trump campaign chairman Paul Manafort Paul John ManafortOur Constitution is under attack by Attorney General William Barr Bannon trial date set in alleged border wall scam Conspicuous by their absence from the Republican Convention MORE.

Former Trump campaign manager Corey Lewandowski Corey R. LewandowskiHow Trump can win reelection: Focus on Democrats, not himself Trump Jr. distances from Bannon group, says he attended 'single' event Bannon, three others charged with defrauding donors of 'We Build The Wall' campaign MORE, however, on Sunday dismissed this possibility for Flynn, stating that the president is not considering a pardon for his former aide.

“But never ever ever has this president said — to the best of my knowledge — that he’s even thinking about a pardon for Mike Flynn,” Lewandowski told “Fox News Sunday.”

Lewandowski also denounced an assertion from former Trump campaign adviser Roger Stone Roger Jason StoneThe agony of justice Our Constitution is under attack by Attorney General William Barr Justice IG investigating Stone sentencing: report MORE, who said in a recent interview that the president's most recent pardon was sending a “signal” to the special counsel.

"Indict people for crimes that don’t pertain to Russian collusion and this is what could happen," Stone told The Washington Post last week.

In a controversial move, the president pardoned conservative commentator Dinesh D'Souza on Thursday, and has floated the idea of pardoning celebrity Martha Stewart and commuting the sentence of former Illinois Gov. Rod Blagojevich (D).

Lewandowski dismissed D'Souza's pardon as a "one-off opportunity."

Trump has issued other pardons during his tenure that have sparked criticism, including pardoning former Maricopa County, Ariz., Sheriff Joe Arpaio and I. Lewis “Scooter” Libby, who was a top adviser to former Vice President Dick Cheney.

But Mueller’s ongoing probe into Russia’s election interference and any potential ties between Trump campaign officials and Moscow has raised alarms that Trump could pardon his allies, or even himself, should he need to do so.

Preet Bharara Preetinder (Preet) Singh BhararaDemocratic attorneys criticize House Judiciary Democrats' questioning of Barr Clyburn echoes calls to rename Pettus bridge Support swells for renaming Edmund Pettus Bridge in Selma to honor John Lewis after his death MORE, the former U.S. attorney for the Southern District of New York — whom Trump fired last year after he refused to resign from his post — said a sitting U.S. president pardoning himself would be “outrageous.”

“I think if the president decided that he was going to pardon himself, I think that it is almost self-executing impeachment,” Bharara told CNN’s “State of the Union.”

“Whether or not there is a minor legal argument that some law professor somewhere in a legal journal can make that the president can pardon, that is not what the Framers could have intended. That's not what the American people, I think, would be able to stand for.”