Gibbs said Nancy Killefer, who was on track to become the federal government's chief performance officer, resigned on Tuesday for similar reasons.
Both of them had a series of problems with their personal finances and failed to pay hundreds of thousands in taxes.
Gibbs said both "recognized you can't set an example of responsiblity but accept a different standard of service" during a White House press briefing Tuesday afternoon.
Obama's Treasury Secretary Tim Geithner, however, also had tax problems. He failed to pay $34,000 in taxes while working for the IMF. Gibbs said Geithner's transgressions were not a deal-breaker because "Mr. Geithner has gone through a process..he has gone through the full Senate with bipartisan support."
Gibbs flailed to answer more pressing why the president stood by Geithner despite his tax problems, but not Daschle. He would not answer a question if Obama would have kept supporting Daschle or Killefer if he had not withdrawn his name.
The most he would say is that there are "a few exceptions for people who are uniquely qualified to lead this country."
"I am not going to spend a lot of time up here today looking in the rear view mirror," he said.
Fed Still Expects Two Hikes, Market Still Says One, Not Until November
Gross Domestic Product
Setting the Record Straight on Great Britain, America and World War II
Victor Davis Hanson
Conservatives for Trump?
BREXIT: Brits Wanting To Leave the EU Spikes After Obama Tried To Convince Them To Stay In It