The House Financial Services Committee plans to hold a hearing on the Wells Fargo mess Thursday. Stumpf has been invited to testify.
"I don't think it's going to be much better for them in front of the House as it was in the Senate last week," bank analyst Paul Miller of FBR Capital Markets told CNBC on Monday. "Hopefully Stumpf is better prepared going into this."
Last week, senators fired questions at Stumpf, centering on why the bank allowed the problems to fester for years before taking action, and called for clawbacks.
Many questions were about Carrie Tolstedt, the Wells Fargo executive in charge of the unit where employees opened as many as 2 million unauthorized customer accounts. She is retiring at the end of the year, according to a bank announcement in July.
Over the course of her career at the bank, Tolstedt accumulated stock and options of $95 million, based on when the stock was trading at around $49 per share, according to a Wells Fargo proxy statement.
"I think [the Wells mess] does have an impact on the stock price. And it's going to continue to have an impact on the stock price until the board makes some type of action here," Miller said on "Squawk on the Street."
Shares of Wells Fargo have fallen nearly 10 percent since the settlement announcement Sept. 8.
"I think it's going to get worse before it gets better," he added.
Miller said investors and regulators want a change in leadership at the top. "They want to turn that page. But as long as Stumpf is there, it's hard."