“Most of this could be absolved or at least elided if President Trump was on board,” said Liam Donovan, a Republican strategist.

But Mr. Donovan acknowledged that Ms. Loeffler was in something of a vise.

“The entire logic of picking Kelly was predicated on ‘we’re losing the suburbs, so you pick a Buckhead mom to win back Buckhead moms,’” he said, alluding to the tony Atlanta enclave. “But that’s only tenable if you don’t have to squander your potential outflanking Doug Collins for Fox News dads.”

Ms. Loeffler’s supporters in Washington want Mr. Trump to understand what he would be risking by abandoning the wealthy Ms. Loeffler: her husband, one top Senate Republican official noted on Friday, just donated $1 million to Mr. Trump’s “super PAC” last month, and the couple have directed tens of thousands of dollars more to key Senate races.