Like McConnell, Graham has the next election at the top of his agenda. But while McConnell has made a conscious decision to ignore Trump and wants the party to move beyond the twice-impeached former president, Graham is trying to engage Trump to help the party’s chances.

“President Trump is the most consequential Republican in the party,” Graham said on Fox. “If Mitch McConnell doesn’t understand that, he’s missing a lot.”

Not every Republican agrees with Graham. Arkansas Gov. Asa Hutchison, a former congressman, told CNN’s Erin Burnett Thursday that Graham is wrong to suggest Trump is essential to the party’s future success.

“Certainly he has a huge following in our party, but he cannot define us for the future,” Hutchison said. “We have to give outreach to the Trump supporters. They’re a huge part of our Republican base, and we have to identify with the issues they are concerned about. But it doesn’t have to be defined by one person.”

Nevertheless, Trump remains the GOP figure whose words and actions reliably command the most attention. And in his lengthy Tuesday statement blasting McConnell, Trump included a veiled threat to support his own candidates in Republican primaries.

“Where necessary and appropriate, I will back primary rivals who espouse Making America Great Again, and our policy of America First,” Trump said.

That possibility concerns many Republicans, especially those who fear the coming GOP primary season could rob them of any chance of winning back the Senate. The worry is that more extreme candidates, boosted by Trump, will win the primaries, but then prove unable to win in the general election against Democrats. This is of particular concern in swing states.

One troublesome example for these Republicans is Arizona Republican party chair Kelli Ward, a Trump favorite. But if she ran for Senate with a Trump endorsement, few think she could go on to beat Democrat Mark Kelly, who is finishing out the late John McCain’s term. To keep his seat, Kelly will have to run in 2022 for a full six-year term of his own.

And there is downright panic among national party leaders that, in Georgia, Rep. Marjorie Taylor Greene will run against former Republican Sen. David Perdue for the Senate seat. The nomination of Greene, who has publicly espoused conspiracy theories in the past, could diminish the Republican Party’s chances of beating Democratic Sen. Raphael Warnock.

GOP sources say convincing Trump either to stay on the sidelines in those two races, or even endorse a candidate like Perdue, would go a long way.

Then there is the question of whether Trump’s influence in the GOP is deterring strong candidates from jumping in at all.

Arizona Gov. Doug Ducey’s term is up after 2022, for example, and many in the party think he has the best shot at beating Kelly for the Senate seat. But Trump turned on Ducey after the governor refused to go along with his lies about the election and certified Joe Biden’s win in Arizona.

Ducey told CNN last month he isn’t running for Senate, but some believe he might change his mind if Trump promises to stay quiet.

And in New Hampshire, Republicans are hoping to lure former Sen. Kelly Ayotte back for another campaign. But she is another person who has clashed with Trump.

Graham may be one of the few people who can persuade Trump. The South Carolina Republican just won reelection to another six-year term in the Senate, and has built up credibility with the former president, who enjoys their friendly competition on the golf course. But Graham — like most who encounter the mercurial former president — has had mixed success in getting through to him.

Once a tough critic of Trump during the 2016 primaries, Graham has found his way into the inner circle — a development that has astounded even him.

CORRECTION: An earlier version of this story misstated the day Scalise met with Trump. They met on Tuesday, not Wednesday.