Massachusetts Senator John Kerry said Mr Daschle's withdrawal was a great loss to the cause of health care reform.
"When the smoke clears and the frenzy has ended, no-one will believe that this unwitting mistake should have erased 30 years of selfless public service and remarkable skill and legislative expertise on health care," he said.
Mr Daschle paid about $128,000 in back taxes and $12,000 in interest last month.
Appearing before the Senate Finance Committee on Monday, he apologised for what he said had been a mistake. The tax issue stemmed from the use of a car and driver provided to him by a friend and consulting client.
The BBC's James Coomarasamy in Washington says Mr Obama has been facing growing criticism over the contradiction between his pledge to create a new, ethical administration and the problems of his nominees.
US Treasury Secretary Timothy Geithner was confirmed last week only after long arguments over his failure to pay $34,000 (£24,500) in taxes he owed until shortly before he was nominated.
In January, New Mexico Governor Bill Richardson announced he was withdrawing from consideration as commerce secretary after an investigation was launched into a state contract that had been given to his campaign donors.
Republican Senator Judd Gregg was on Tuesday nominated instead, the second from his party to be asked to join Mr Obama's cabinet.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.