Senator Lindsey Graham admitted the Republicans had no "smoking gun" with which to tie Joe Biden to his son, Hunter's, business dealings.
That didn't sit well with Congresswoman Marjorie Taylor Greene, who called for another conservative to primary the senator during his next election.
"I think somebody else better run for senator in South Carolina," she said during a Turning Points USA (TPUSA) Action event.
Mr Graham made his remarks during an appearance on “Meet the Press”, where he largely dismissed the GOP's efforts to impeach Mr Biden.
"You know, I haven't really been paying that much attention to it. They have to prove that President Biden somehow financially benefited from the business enterprises of Hunter Biden. We'll see," Mr Graham said on Sunday. "If there were a smoking gun, I think we'd be talking about it."
Ms Greene and other MAGA Republicans have been waiting for a Republican House majority to impeach Mr Biden.
"How can Lindsey Graham in Washington DC on ‘Meet the Press’ say that he hasn't seen a smoking gun of evidence? That he doesn't think that we produced enough evidence to impeach Joe Biden?" she said during the TPUSA event.
She then asked the audience — filled with TPUSA ideological supporters who she called "the American people" — if they thought Republicans had enough evidence to impeach the president. They cheered in agreement.
That's when she suggested someone should primary Mr Graham.
The South Carolina senator continually places himself on a tightrope between MAGA conservative ideology and more traditional Republican ideas, which has left him unpopular in both worlds.
He was booed in his home state earlier this year when called to stand before a rally audience by former President Donald Trump. Mr Trump tried to explain that Mr Graham is helpful to his needs when they need to get "the left" on board with legislation.
But before Mr Trump took office, he was staunchly opposed to the real estate mogul's involvement in politics, once claiming the best way to "Make America Great Again" was by telling "Donald Trump to go to hell."
Just after the Capitol riot, Mr Graham reportedly said that Mr Biden — who he formerly called "as good a man as God ever created" — was the "best person to have" leading the nation, according to audio recordings released by authors Jonathan Martin and Alex Burns.
But that was only after he publicly said that Mr Trump should not concede after it was determined that Mr Biden had won the 2020 election.
Regardless of Mr Graham's concerns that the inquiry lacks evidence tying Mr Biden to his son's financial dealings, House Republicans have already voted unanimously to proceed. However, the expulsion of Congressman George Santos and the forthcoming exit of Congressman Kevin McCarthy will leave the House Republicans with only a razor-thin majority to actually impeach Mr Biden.