“The Democrats have stated strongly that they won’t approve a Payroll Tax Cut (too bad!)” Mr. Trump wrote, adding, “The Republicans, therefore, didn’t want to ask for it.”

In truth, it was Republicans who were not interested in a tax cut they saw as ineffective.

They rejected the administration’s plan to omit money for coronavirus testing — an effort many senior Republicans see as crucial to reopening the country and stabilizing the economy — and to defund schools that fail to resume in-person classes in the fall. And on Thursday, they were resisting Mr. Trump’s attempts to use the measure as a vehicle to address one of his longtime obsessions: the F.B.I.’s Brutalist-style headquarters in downtown Washington, situated across the street from his luxury hotel…

Even as they privately haggled over the aid bill on Thursday, Republicans publicly defied Mr. Trump on another matter, voting for the annual military policy bill that he has threatened to veto over its requirement that the Pentagon rename bases named for Confederate figures. Many Republicans believed his stance was out of step with public opinion amid a nationwide conversation about racism in the United States.