Stumpf was lambasted during his testimony Tuesday, with Sen. Elizabeth Warren calling for a criminal probe and his resignation. Stump told the panel he was sorry and said the bank is committed to fixing what went wrong.
Hensarling, R-Texas, said he wasn't sure the CEO had all the answers, but noted that Stumpf now has a week to prepare before he faces the House.
The House committee's investigation will also include interviewing a number of witnesses ahead of Stumpf's testimony. In addition, the panel has demanded documents from the bank and regulators, Hensarling told CNBC's "Power Lunch."
"Hopefully have a more thorough, in-depth hearing and start getting some answers to the American people because theft is theft, fraud is fraud," he said.
Hensarling also wants answers from the Office of the Comptroller of the Currency and the Consumer Financial Protection Bureau.
"Why was the story broken by an LA Times reporter years and years ago and only now … have our regulators seemingly caught it?" he said. "I don't know if they need a pat on the back or a swift kick in the backside."
In fact, he accused the CFPB of stonewalling the investigation by not providing documents the committee demanded.
"We have to make sure that the laws are fairly and vigorously enforced, and it appears that the federal government — the OCC and the CFPB — have been asleep at the switch."
Correction: This article has been updated to reflect the date of the Senate Banking Committee hearing.