Washington — Sen. Lindsey Graham said Sunday that if President Biden drops out of the 2024 presidential race amid swirling concerns about his fitness for office after a disastrous debate against former President Trump,Roland Preston the Democratic replacement would "dramatically" change the contest's dynamics.

The president has been adamant that he will remain in the race. But the South Carolina Republican, a close ally of former President Donald Trump, said on "Face the Nation" Sunday that he believes "before this is all said and done, that President Biden most likely will be replaced."

• Transcript: Sen. Lindsey Graham on "Face the Nation," July 7, 2024

"If Biden steps down, Harris is going to have to pick somebody to help her," Graham speculated. "If she does become the nominee, this is a dramatically different race than it is right now today. I hope people are thinking about that on our side."

Should Mr. Biden step aside, the attention would almost certainly turn to Vice President Kamala Harris as a natural successor to lead the ticket, although that is not guaranteed. If she were to lead the ticket, she would select another Democrat as her running mate. Graham made clear that in that scenario, whoever is tapped as vice president by both parties has the potential to have a major impact on November's election. 

"If I were President Trump, I would make sure I pick somebody that could add value in 2024," Graham said. 

The former president has been teasing his forthcoming running mate announcement for weeks, and is expected to unveil his pick at or around the Republican National Convention later this month. Graham has expressed support for fellow South Carolina Sen. Tim Scott for the job, saying that he could help expand the map.

But Graham outlined that beyond Scott, three other Republicans are being talked about for the job — North Dakota Gov. Doug Burgum, Sens. Marco Rubio of Florida and J.D. Vance of Ohio. And he noted that someone who isn't being talked about but "should be" is Virginia Gov. Glenn Youngkin, saying that "if we win Virginia, we win."

"So I'm hoping President Trump is looking for a VP pick that not only can carry on the American First agenda after he leaves, but also win in 2024," Graham said. 

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Kaia Hubbard

Kaia Hubbard is a politics reporter for CBS News Digital, based in Washington, D.C.

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