Even Obama has been critical, insisting Monday that there's "no excuse for the problems." But he also said the problems should not amount to a blanket condemnation of the ACA.
"Nobody's madder than me about the website not working as well as it should," Obama said, "which means it's going to get fixed."
Calls for resignation
Several top Republicans -- including 2012 vice presidential nominee Rep. Paul Ryan -- have called on Sebelius herself to step down due to the program's problems. The secretary skirted questions Tuesday about whether she'd step down, saying only that she works "at the pleasure of the president" and is committed to her job.
"I think my job is to get this fully implemented and to get the website working right," Sebelius told Gupta.
Billionaire investor Warren Buffett stood up for Sebelius in an interview with CNN's Piers Morgan on Tuesday night.
"I am a friend of Kathleen's, and I'm a friend of her when she's in trouble," Buffett said. "I like Kathleen. I feel sorry for her in the position she's in. Obviously, it's a huge screw up, but it will get worked out."
Sebelius refused to give a timetable Tuesday as to when the website will be fully operational, but insisted it's improving every day.
"More people are having an easier time," she said, "and we intend to stay at this until we open the door's wide open."
And it's too early to call the rollout a failure, the health secretary argued. There's still a long time for people to take advantage in person, by calling or by using the website during the open-enrollment period.
When that six-month stretch is over, Sebelius said, people can better decide whether this part of the ACA is a success or a failure.