But there was Mr. Cotton on “Fox & Friends” last week, pushing the idea of a quick cash infusion to counter the economic devastation of the coronavirus outbreak. A few hours later, Senator Mitt Romney, Republican of Utah, proposed on Twitter that “every American adult should immediately receive a one-time check for $1,000.” The idea was first met with skepticism and even incredulity.

But as it became clear there was bipartisan opposition to President Trump’s push for a payroll tax holiday, Mr. Mnuchin got onboard and the cash idea quickly transformed from pipe dream to reality, to the centerpiece of Senate Republicans’ roughly $1 trillion rescue plan. The optics were jarring, since it is Republicans who usually accuse Democrats of being too quick to throw taxpayer money around.

“Senate Republicans want to put cash in Americans’ hands,” Mr. McConnell said on the Senate floor as colleagues of both parties worked behind closed doors to hammer out the details of the economic stabilization plan.

Not everyone was as enthusiastic about the cash payments. Some Republican colleagues balked, Democrats had reservations about the scope and distribution of the payments and conservative fiscal watchdog groups were aghast.

David McIntosh, the head of the free-market Club for Growth, said Republicans seemed to have borrowed the idea from Andrew Yang, the former Democratic presidential candidate who proposed a $1,000 universal monthly income. The idea, Mr. McIntosh noted, was ridiculed by Republicans just a few weeks ago.

“It is panic-driven — panic on Capitol Hill,” Mr. McIntosh said. “There is no indication it would work or make a difference. They are throwing up any idea.”

Under the Senate Republicans’ original bill, individuals could receive one-time checks of a maximum of $1,200 or $2,400 for married couples, in addition to $500 a child. Those earning more money would get a bigger check, and the payment would phase out for those earning more than $75,000, ending entirely for taxpayers with more than $99,000 in income or families earning $198,000. The initial Senate measure would also reduce the payments to $600 for people with no income tax liability but at least $2,500 in earnings.