But their ties to Trump – whose grip on the Republican Party has strengthened through a wave of primary victories – vary.
Barrasso, the No 3 Republican, backed Trump in early January, nearly a week before the January 15 Iowa caucus, and drew effusive praise from the Republican front-runner.
Cornyn, a longtime McConnell ally, fell in line after Trump soundly won the January 23 New Hampshire primary, calling on his colleagues to consolidate their support.
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Thune, who initially supported Senator Tim Scott for president, didn’t heed that advice until just days ago.
He’s long been seen as McConnell’s heir apparent, but the belated endorsement – coupled with criticisms of Trump after the January 6, 2021 attack on the Capitol – could put him at a disadvantage.
Republican senators, however, could also decide they want a buffer between them and Trump, not just a cheerleader. Several criticised Trump after the Capitol insurrection. And the vast majority voted to certify the 2020 election Trump continues to baselessly claim was stolen from him.
None of the Johns have announced their candidacy, but they’ve all said they’ll talk to colleagues.
“I’ve made no secret of my intentions,” Cornyn told reporters.
With months to go until the election, other candidates could emerge. Steve Daines of Montana leads the party’s campaign committee and could stake a claim for the top job if the party does well in November.
Daines, an earlier endorser of Trump, has had a productive relationship with the former president in helping avoid bloody primaries in states like Montana and West Virginia. Daines declined to say if he’s interested Wednesday.
McConnell has become the last serious bulwark within the party against Trump populists’ animosity toward US international commitments. The race to replace him will be a referendum on where the Republican Party stands on foreign aid and the importance of US alliances.
Thune and Cornyn both were among the 22 Senate Republicans who backed the US$95 billion supplemental spending package for Ukraine, Israel and other issues after a border compromise McConnell had nurtured for months fell apart under attacks from Trump and House Speaker Mike Johnson.
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Barrasso and Daines voted with the majority of Republicans against that package. Barrasso has generally struck a more conservative line, more in line with Trump and against a series of bipartisan deals signed by US President Joe Biden.
Whoever becomes leader will have to contend with party splits between a corporate-friendly establishment represented by McConnell and the emerging populist wing led by younger senators like JD Vance and Josh Hawley.
Cornyn, who previously kept tabs on Republican senators’ likely votes on legislation as party whip, has built up a reputation as a conservative deal-cutter in the Senate.
His handiwork has included crafting an update to gun laws after the mass shooting in Uvalde, Texas, and helping pass a massive package of semiconductor manufacturing subsidies.