“They asked substantive, tough questions,” Sam Bell, the founder of Employ America, said of the Republican senators. Mr. Bell’s group has been pushing for Fed nominees who are focused on lifting employment and has vocally opposed Ms. Shelton.

“The aura, after the hearing, is that there’s serious bipartisan skepticism,” he said.

Democrats showed their discomfort with Ms. Shelton, particularly her close ties to Mr. Trump, and pressed her repeatedly on whether she would operate independently of the White House. They quizzed her on whether she felt the president’s frequent attacks on Jerome H. Powell, the chairman of the Federal Reserve, were appropriate.

“Frankly, no one tells me what to do,” Ms. Shelton said at one point. “I don’t think it’s the job of the Federal Reserve to accommodate political agendas” and “the Fed operates independently, as it should.”

But she indicated that she did not have a problem with Mr. Trump’s criticisms of Mr. Powell. The president regularly blasts the Fed chair on Twitter and in public remarks, faulting him for not doing more to lift the economy and pushing him to cut interest rates more aggressively.

“I do believe that every American, every member of Congress” and “our president” have the right to criticize the Fed, she said, adding later that “in some ways, it’s refreshing that it is out in the open.”

Ms. Shelton’s nomination has raised concerns among economists and former central bankers, who worry that her changing policy views — she used to support higher interest rates, but flipped to support lower rates around the time Mr. Trump took office — suggest that she would operate with an eye on the White House.

Heightening that concern is the possibility that Ms. Shelton is viewed as a possible successor to Mr. Powell, Mr. Trump’s first pick for the chair job, should the president win a second term and opt to replace him.