If you doubt the power of Donald Trump’s endorsement, look no further than the Ohio Senate race.

Since April 15, when Trump backed J.D. Vance in the Republican primary, the venture capitalist and author of “Hillbilly Elegy” has zoomed to the top of the public polls. Vance jumped from 11 percent of likely voters in March to 23 percent now, according to Fox News.

The real test of Trump’s party boss mojo, however, is fast approaching: actual elections, beginning with Ohio’s on Tuesday. Trump has endorsed candidates in at least 40 Republican primaries that are taking place in May, my colleague Alyce McFadden has tabulated. Most of these contests involve an incumbent who faces no serious challenger. But in statewide races from Pennsylvania to Georgia and Idaho to North Carolina, Trump’s imprimatur could prove decisive.

Republicans are watching these races closely for signs that Trump’s hold over the party is waning. Privately, many G.O.P. operatives view the former president as a liability. And while he has shown a unique ability to energize the party’s base and turn out new voters, those operatives are still dreading the likelihood that he runs again in 2024, anchoring candidates up and down the ballot to an erratic, divisive figure who was rejected by swing voters in 2020.