The former president faces several potential Republican challengers in his bid for the White House. Donald J. Trump refused to say he would support the next Republican presidential nominee if it was not him, exposing a potential quagmire along the party’s path toward reclaiming the White House in 2024 and showcasing, once again, the former president’s transactional spin on political loyalty.In a radio interview on Thursday, the conservative commentator Hugh Hewitt asked Mr. Trump if he would support “whoever” wins the party’s nomination next year. Mr. Trump announced his third presidential campaign in November and faces a number of potential Republican challengers.“It would depend,” Mr. Trump said, adding, “It would have to depend on who the nominee was.”The hesitation from Mr. Trump differed from many of the Republican Party’s top officials and most prominent activists. Several of Mr. Trump’s critics inside the party, including Senator Mitch McConnell of Kentucky, the minority leader, have repeatedly said they planned to back the G.O.P. nominee, even if that person is not their top choice.William P. Barr, who served as attorney general during the Trump administration, called Mr. Trump’s tactics “extortion” in an interview last August with Bari Weiss, a political writer and commentator. “What other great leader has done this? Telling the party, ‘If it’s not me, I’m going to ruin your election chances by telling my base to sit home. And I’ll sabotage whoever you nominate other than me.’ It shows what he’s all about,” Mr. Barr said. “He’s all about himself.”Minutes before Mr. Trump’s interview on Thursday, Larry Hogan, a Republican who is the former Maryland governor and a consistent Trump antagonist, said on the same radio program that he would back the Republican nominee.The Run-Up to the 2024 ElectionThe jockeying for the next presidential race is already underway.G.O.P. Field: Nikki Haley is expected to join the contest for the Republican Party’s nomination soon, but other contenders are taking a wait-and-see approach before challenging former President Donald J. Trump.Trump’s Slow Start: In the first weeks of his third presidential campaign, Mr. Trump notched a less-than-stellar fund-raising haul, yet another signal that his hold on some conservatives may be loosening.Democrats’ Primary Calendar: A plan spearheaded by President Biden could lead to a major overhaul of the party’s primary process by making South Carolina — instead of Iowa — the first nominating state.A Looming Issue: As Mr. Biden sharpens his economic message ahead of a likely re-election bid, the case over his handling of classified documents has thrust him into an uncomfortable position.“I imagine that will be the case,” Mr. Hogan said when asked if he would “support whoever the nominee of the Republican Party is in 2024.”Mr. Hewitt pressed the former governor on whether he would even back Mr. Trump’s nomination.“I just don’t think he’s going to be the nominee, but I’ll support the nominee,” Mr. Hogan said.The frequent explanation for partisan loyalty like Mr. Hogan’s is that winning a national election in a country increasingly divided between Republicans and Democrats is nearly impossible without a completely unified party. In 2020, for example, about 9 percent of Republicans voted for someone other than Mr. Trump, compared with just 3 percent of Democrats who voted for someone other than their nominee, Joseph R. Biden Jr., according to AP VoteCast, a study of the 2020 electorate conducted for The Associated Press by NORC at the University of Chicago.This week, a poll from The Bulwark, a conservative anti-Trump website, found that most Republicans wanted someone other than Mr. Trump to be the party’s next presidential nominee. But that same poll showed that 28 percent of Republican voters would be willing to back Mr. Trump in an independent bid.An independent campaign from Mr. Trump would splinter the Republican base and all but ensure another four years for Democrats in the White House. Mr. Trump, who has been registered in the past as a Democrat and a Republican, considered running for the Reform Party’s presidential nomination in 2000.Mr. Trump has long viewed politics through a personal lens, equating disagreements with his policies and tactics to a lack of allegiance to conservatism as a whole. One of the former president’s favored put-downs of opponents inside his party is to dismiss them as “RINOs,” or Republicans in name only.Even loyalty to Mr. Trump and his personal brand of Republicanism has often not been enough to avoid being crushed by the former president’s dominating style of politics.In primaries last year, Mr. Trump refused to back campaigns for numerous longtime supporters and former officials in his administration — including Lou Barletta’s campaign for governor of Pennsylvania — over candidates who appeared more likely to win.Mr. Barletta, a former congressman, was one of Mr. Trump’s earliest supporters in Congress in 2016, but the former president instead endorsed State Senator Doug Mastriano. Mr. Mastriano was leading in the primary polls but lost in the general election to the Democrat, Josh Shapiro, by double digits.In the 2016 race, Mr. Trump was also initially unwilling to say whether he would back the eventual Republican nominee, a source of deep alarm to party leaders and officials. During a Republican debate in August 2015, Mr. Trump was the only one of 10 candidates onstage who refused to pledge support to the eventual nominee — and the only one not to rule out a third-party bid.At the time, Mr. Trump said his decision would depend on how the Republican Party treated him.A month later, he declared he was being treated fairly by the party, and signed a pledge to support the eventual nominee during a private meeting at his Trump Tower office with Reince Priebus, who, at the time, was chairman of the Republican National Committee.Mr. Trump then hosted a news conference in the lobby of Trump Tower. Mr. Priebus did not attend, despite Mr. Trump’s insistence.Maggie Haberman More