In an appearance on Fox News, Obama said he takes responsibility for Daschle's nomination process, which ended this week with the South Dakota Democrat withdrawing his name for consideration to lead the U.S. Department of Health and Human Services.
Daschle's nomination amid revelations he failed to pay $134,000 in federal taxes and has since paid $146,000 in back payments and interest.
"I consider this a mistake on my part, one that I intend to fix and correct and make sure that we're not screwing up again," Obama said. "Ultimately I have to take responsibility for a process that resulted in us not having a (health and human services) secretary at a time when people need relief on their healthcare costs."
On Monday, Obama had said he "absolutely" stood by his close friend despite the revelations.
Daschle had met behind closed doors Monday with the Senate Finance Committee, and had been scheduled to appear before the committee next week for his confirmation hearing.
But Tuesday, he issued a statement, saying the position and the work required "will require a leader who can operate with the full faith of Congress ... without distraction."
"Right now, I am not that leader," Daschle said.
Daschle was the second person Tuesday to ask their name be withdrawn from an administration post. Nancy Killefer withdrew her name from consideration to be the first U.S. chief performance officer because of tax issues.