Already, two of Mr. Trump’s early and most prominent Senate endorsements have backfired long before voters head to the polls. In addition to Alabama, his initial choice in Pennsylvania, Sean Parnell, quit the race last fall after abuse allegations emerged in a child custody dispute. And fears of further setbacks have helped keep Mr. Trump on the sidelines so far in choosing a replacement there or a candidate in the Ohio or Missouri Senate races.

Georgia, where Mr. Trump is headed this weekend, represents one of his riskiest bets. He has been fixated on unseating the Republican governor, Brian Kemp. But Mr. Trump’s handpicked challenger has been struggling to gain traction against the well-financed governor less than two months before the primary.

“I don’t know whether he is letting emotion rule his decision making or if he is getting bad advice,” said Glen Bolger, a Republican pollster, “but it seems like he is picking candidates who are pretty weak, and that’s not a place — when you’re trying to be kingpin — where you want to be.” He added that Mr. Trump’s image remained “very strong” among Republican primary voters.