Like many of Ms. Shelton’s policy views, her thoughts on excess reserves are not fully consistent with what Mr. Trump says he wants.

The president has said the Fed should lower rates, stop shrinking its balance sheet and start expanding it again by buying more bonds — a practice that’s often called quantitative easing or Q.E.

Ms. Shelton’s plan would involve the Fed dropping rates to zero. But to ditch paying interest on reserves, the Fed would also need to slash its bond holdings, because the old rate-setting system does not work when there is a lot of money sloshing around the financial system.

In other words: The country can have its old operating framework or a big balance sheet, but probably not both.

“If you’re in favor of Q.E., then presumably you’re in favor of interest on excess reserves — it’d be hard to argue how you could do one without the other,” said William Dudley, former president of the Federal Reserve Bank of New York. The current system will make it easier for the Fed to go back to buying bonds should the economy enter another downturn, he said, leaving policy more nimble. It also makes setting interest rates easier.

Such arguments have failed to placate lawmakers in the past. In a rare show of bipartisan sentiment in February 2016, Jeb Hensarling, then the Republican chairman of the House Financial Services Committee, and Maxine Waters, the top Democrat on the panel, criticized Janet L. Yellen, the Fed chair at the time, for the practice. Ms. Waters walked her critiques back, but in 2017, Mr. Hensarling again urged that it “should not become a permanent tool of monetary policy.”

Lawmakers have stopped blasting the practice so loudly since Jerome H. Powell took over at the central bank in early 2018. The Fed announced this year that it would continue using the interest-on-reserves approach to setting interest rates indefinitely — allowing officials to stop shrinking their balance sheet earlier.