Federal Reserve Chair Janet Yellen’s defense of the central bank as nonpartisan came under attack on Wednesday, as a Republican congressman cornered her on whether a key policy maker would have a conflict of interest in discussing a post in the next US president’s administration.

Fed Governor Lael Brainard has donated to Clinton’s campaign and is widely viewed as a potential Clinton pick for Treasury secretary. Yellen hesitated and then demurred when Representative Scott Garrett of New Jersey asked whether Brainard would have a conflict of interest if she were indeed in talks with Democratic nominee Hillary Clinton’s campaign about a position. The election is Nov. 8.

‘‘I would have to consult my counsel, I’m not aware that that’s a conflict,’’ Yellen said in testimony to the House Financial Services Committee in Washington, while rejecting Garrett’s suggestion that the US central bank has a political bias.

A Fed spokeswoman later said that Brainard hasn’t been in conversations with either political campaign.

The heated exchange followed Republican presidential nominee Donald Trump’s comment, heard by tens of millions of Americans in Monday’s debate, that the Fed is keeping rates low to make President Obama look good. Merited or not, the persistent questioning of the Fed’s objectivity — and Yellen’s inability to deflect that skepticism — could provide more of an opening for congressional efforts to reshape the central bank’s governance or how it sets monetary policy.

‘‘The accusations today, that there could be negotiations going on, it’s the last thing the Fed needs,’’ said Sarah Binder, a senior fellow at the Brookings Institution in Washington who studies politics and the central bank. ‘‘The more the attacks, the weaker the Fed — it makes it harder for the Fed to fend off changes.’’

Appearance issues matter for the Fed because ‘‘Congress is the boss,’’ Binder said. ‘‘The optics do not look good at all — it puts a little tinder on the fire that these lawmakers, particularly the House Republicans, have been lighting,’’ she said.

Yellen said that ‘‘what’s important to me is whether or not, in our decision-making, our collective decision-making, I see politics being brought to bear in reasoning about our decisions, and I have never seen that with any of my colleagues.’’

The Fed chair told Garrett during their discussion that the Hatch Act, which limits the political activities of some government employees, doesn’t prohibit Fed officials from donating to political campaigns. Brainard, a former Treasury undersecretary for international affairs under Obama, has given $2,700 to Clinton’s campaign, according to Federal Election Commission records.

The back-and-forth over Brainard’s possible contact with the campaign was a flashpoint at a hearing where the Fed’s relationship to politics was a frequent topic. Democrats Carolyn Maloney and Gregory Meeks both emphasized that the Fed is nonpartisan, while Garrett said there’s an unacceptable ‘‘cozy relationship’’ between the Fed and the administration.

Garrett was implying ‘‘that somehow this administration was wrong in working with Ms. Yellen,’’ California Representative Maxine Waters, the ranking Democrat on the financial services panel, said on Bloomberg Television after the hearing. ‘‘I don’t think that Mr. Garrett had a real point, a credible point.’’

Political histories are common at the Fed, from both sides of the aisle. Yellen chaired President Bill Clinton’s Council of Economic Advisers from 1997 to 1999, while her Fed predecessor, Ben Bernanke, previously headed the council during Republican George W. Bush’s administration. Alan Greenspan, Fed chairman from 1987 to 2006, was also a Council of Economic Advisers chairman during Republican Gerald Ford’s administration.

Likewise, it isn’t unprecedented for Fed officials to have contact with political campaigns as personnel decisions are being decided.

In his memoir, Timothy Geithner recalls meeting with then-Senator Obama in his room at the W Hotel in midtown Manhattan before the 2008 election, where the future president suggested that he might ask Geithner — then head of the New York Fed — to come to Washington as Treasury secretary. That meeting was in mid-October; Geithner voted at the next Fed meeting, at the end of the month, to cut interest rates by a half percentage point amid the deepening financial crisis.

Geithner later flew to Chicago to meet with Obama again in early November. Several weeks later, once the appointment was officially announced, Geithner left the Fed’s rate-setting committee.

Normal or not, the perception of political coziness isn’t good for the central bank.

‘‘They don’t want to be viewed as political, for certain,’’ said Sam Bullard, senior economist at Wells Fargo Securities LLC in Charlotte, N.C. ‘‘They want to be removed from the process and be viewed as a group that is clearly doing the best it can to help the US economy.’’’