"I don't want to send a message to the American people that there are two sets of standards, one for powerful people, and one for ordinary folks who are working every day and paying their taxes," Obama later told CNN.
"I think this was a mistake ... and we're going to make sure we fix it so it doesn't happen again."
Daschle said he withdrew because he did not want the tax issue to become a "distraction" for Obama's health care 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 still had "confidence" in the other people he had chosen to serve in government and defended the administration's vetting process.
Tim Geithner, Obama's nomination for treasury secretary, barely survived a controversy over his own unpaid taxes, before eventually being sworn in last week.
The withdrawals of Daschle and Killefer come only weeks after Bill Richardson, the governor of New Mexico, pulled out of consideration for the job of US commerce secretary after it emerged he was the subject of a probe into a state contract awarded to his political donors.
The controversy comes as Obama is urging the US senate to approve a $900bn economic stimulus bill despite stiff opposition from US Republicans.
He warned US Congress on Tuesday that the final version of the economic recovery package - currently being debated in the US senate - should not include
protectionist language that could trigger a trade war.
Obama was referring to a controversial "buy American'' provision in the package, which states that all materials for the bill's reconstruction plans be from US companies.
The proposal has led to accusations from other nations of economic protectionism.