The bank has come under fire in recent days after it was revealed its staff signed customers up for products without their consent. Earlier this month, Wells Fargo was hit with a $100m (£76.7m) fine for secretly opening accounts which were not authorised by customers, the largest penalty from the Consumer Financial Protection Bureau to date.
The bank has also been told to pay $35m to the Office of the Comptroller of the Currency, and an additional $50m to the City and County of Los Angeles.
Stumpf today said he was "deeply sorry" for what had happened and that the incident had pained him more than anything else that had happened during his almost 35 years at the bank. However, he also noted the bank had never instructed its employees to open products for customers in such a manner.
Stumpf later added the bank, which has previously built a positive reputation for successfully cross-selling to customers, now had various controls in place, such as contacting customers after a product had been opened in their name, to make sure a similar problem would not occur today. He added the bank was currently in the process of contacting all of its credit card and deposit customers to check their account was setup legitimately.
However, the senators accused Stumpf's bank of nurturing a culture which encouraged such fraud through low wages, sales targets and pushy management.
In particular, Senator Warren slammed Stumpf for personally profiting from the scandal, as he frequently highlighted the strength of cross-selling activities in investor calls and watched the value of the shares he owned soar during that time period. She called on Stumpf to resign.
Although shares are currently trading up 0.9 per cent at $46.44, this is a significant drop from the $47.13 they opened at this morning and around five per cent lower than the $49.09 they were trading at before the news of the fine broke.
"To save the reputation of the bank, and his own job, Stumpf will need to do show there is some accountability," pointed out Jasper Lawler, market analyst at CMC Markets. "The politicians will want a scalp."