Michael Greenberger, a law professor at the University of Maryland who was an adviser on financial regulation to former President Bill Clinton and helped craft some of the Dodd-Frank legislation in 2010, said he remembered Mr. Barr as being resistant to the more strident limitations lawmakers wanted to impose on big banks. Mr. Greenberger said community groups and academics he is in touch with also don’t like that Mr. Barr opposed a stricter version of the Volcker Rule, which bans banks from making risky bets with depositors’ money.

“Michael Barr is a very bright, well-informed, knowledgeable expert on financial markets, but he and Geithner were not aggressive pushers of Dodd-Frank as it moved through Congress,” Mr. Greenberger said. “In the last few days, the sudden hesitancy about Barr is focused on what he did with Volcker.”

Other opponents of Mr. Barr are focused on his ties to fintech firms. From 2015 to 2017, Mr. Barr served on an advisory board for Ripple, which uses digital currency to transfer payments around the world. Mr. Barr was long gone when, last month, Ripple and its two top executives were sued by the Securities and Exchange Commission for selling unregistered securities in the form of digital currency to raise money for the company’s operations.