He had earlier said in a statement he accepted Daschle's withdrawal with "sadness and regret" but said the government "must move forward".
Daschle said he withdrew because he did not want the tax issue to become "distraction" for Obama's healthcare reform plans, as questions were also asked over his ties to the health lobbying industry.
Robert Gibbs, the White House press secretary, said both former nominees "recognised that you can't set an example of responsibility but accept a different standard of who serves".
Gibbs also said that Obama the president still had "confidence" in the other people he had chosen to serve in government and defended the administration's vetting process.
However he also said the US president "takes responsibility" for the nomination problems.
Daschle and Killefer's moves come only weeks after Bill Richardson, the governor of New Mexico, withdrew his name from consideration as commerce secretary after it emerged he was the subject of a probe into a state contract awarded to his political donors.
And Tim Geithner, Obama's nomination for treasury secretary, had earlier only just survived a controversy over his own unpaid taxes, before eventually being sworn in last week.
It also comes as Obama is urging the US senate to approve a $900bn economic stimulus bill despite stiff opposition from US Republicans.