"did not get a signal" from the White House to step aside, the spokesman said.
Daschle is the third high-profile Obama nominee to bow out. Obama tapped Bill Richardson to be Commerce secretary, but the New Mexico governor withdrew amid a grand jury investigation into a state contract awarded to his political donors. Obama named Republican Sen. Judd Gregg of New Hampshire to the position Tuesday.
Last week, the Senate confirmed Timothy Geithner as treasury secretary, but only after days of controversy over the fact that he had only belatedly paid $34,000 in income taxes.
Asked whether tax questions are going to arise with any other nominees, Gibbs said only that "the president has confidence in the people he has chosen to serve in government." He also defended the administration's vetting process.
He added: "the president takes responsibility" for the spate of nomination troubles.
The White House dispatched senior adviser David Axelrod to Capitol Hill to soothe Democrats whose nerves were frayed by the loss of Daschle.
Obama, Vice President Joe Biden and Daschle's former Democratic colleagues had rallied to Daschle's defense in the wake of questions about his failure to fully pay his taxes from 2005 through 2007. Last month, he paid $128,203 in back taxes and $11,964 in interest.
"Tom made a mistake, which he has openly acknowledged," Obama said Tuesday. "He has not excused it, nor do I. But that mistake and this decision cannot diminish the many contributions Tom has made to this country."
"I was a little stunned. I thought he was going to get confirmed," said Max Baucus, D-Mont., chairman of the Senate Finance Committee, the panel that would have voted on Daschle's nomination. "It's regrettable. He's a very good man."
Daschle also was facing questions about potential conflicts of interests related to speaking fees he accepted from health care interests. He also provided advice to health insurers and hospitals through his post-Senate work at a law firm.
The controversy has undercut Obama's promise to run a more ethical, responsible and special interest-free administration. Republicans and major newspapers had been questioning Obama's decision to stick with Daschle.