It is unclear how much leverage such a universally unpopular proposal would have provided Republicans, who are seeking to counter the Democratic plan by slashing the extra unemployment payments and have omitted funding for state and local governments as well as money to help states carry out the general election amid the pandemic. Both proposals would send another round of $1,200 direct payments to many Americans.
An official familiar with the negotiations said that Republican senators, mindful that it had already taken days to reach consensus among themselves on an opening bid, ultimately stopped resisting the administration’s insistence on including the F.B.I. provision in order to move on to what are expected to be much more fraught negotiations with Democrats, who have been publicly united behind their proposal since May.
A chorus of Republican lawmakers said they were bemused by the demand for the F.B.I. building, particularly given the amount of energy that they had spent hammering Democrats for including items they deemed unrelated to the coronavirus in their opening offer.
“I just don’t get it — how is it tied to coronavirus?” said Senator Rick Scott, Republican of Florida. “I never understood why you’re giving money to the Kennedy Center or National Endowment for the Arts. During a pandemic, let’s focus on solving the problem.”
Senator Mike Braun, Republican of Indiana, was also left bewildered.
“Even if the White House wanted it, I’d be against it because that’s certainly not necessary,” Mr. Braun told reporters.
For some Republicans, it was just another aspect of a proposal they regarded as deeply flawed.
“I’m not inclined to support it now — it’s a mess,” said Senator Josh Hawley, Republican of Missouri, said of his party’s plan. “I can’t figure out what this bill is about. I don’t know what we’re trying to accomplish with it.”
Mr. Mnuchin’s negotiation skills have drawn skepticism from some Republicans, who have fretted privately that he has been too open to making concessions to Democrats in earlier rounds of pandemic aid talks. Asked on Tuesday if the money should remain in the legislation, Mr. Mnuchin told reporters, “We’ll look at everything in the bill.”