Senate Republicans have proposed giving the Federal Reserve access to $425 billion in funding that it could use to extend emergency support to flailing businesses or struggling localities — an approach that would keep central bankers at the center of the coronavirus economic response in ways that could prove politically fraught.

Republican lawmakers proposed increasing a Treasury Department fund that would be used to cover losses on the Fed’s emergency lending programs as part of a sweeping government rescue package. While their effort to advance the bill failed on Sunday evening, it is likely a template for what lawmakers will eventually approve.

Republicans view the Fed as a key player in offsetting the economic havoc being wrought by the coronavirus. That is partly because the Fed can take a limited amount of funds and deploy them widely: The central bank only needs the funds as a guarantee against losses, meaning the $425 billion could be leveraged to support far bigger programs. Treasury Secretary Steven Mnuchin on Sunday seemed to suggest that the backstops could amount to $4 trillion.

“We can lever up to $4 trillion to help everything from small business to big business get through the next 90 to 120 days as we win this war,” he said on Fox News.