Departing Health and Human Services Secretary Kathleen Sebelius insisted in a television interview broadcast Sunday that she was not pushed out of her job and she reflected on the troubled launch of the health-care Web site, which she characterized as "terribly flawed and terribly difficult."

In an interview with NBC News that aired during "Meet The Press," Sebelius said she was not pressured to resign; rather, she established her own timeline for departing the job she has done for about five years. She also acknowledged the problems with the health-care law's implementation, which she said were the most trying of her tenure.

"Well, I would say that the eight weeks where the site was not functioning well for the vast majority of people was a pretty dismal time," said Sebelius. "And I was, frankly, hoping and watching and measuring the benchmarks. But, having failed once at the front of October, the first of December became a critical juncture."

The Obama administration's belief that the Web site for Americans can sign up for coverage would be ready by Oct. 1 "was just flat-out wrong," Sebelius said.

Sebelius announced her resignation last week. Obama nominated Office of Management and Budget Director Sylvia Mathews Burwell to replace her. The former Kansas governor said she saw the end of the health-care open enrollment period as a prudent time to exit.

"There is never a good time," said Sebelius. "There's going to be another open enrollment. There are changes down the road. But the president and I began to talk, you know, after the first of the year. And I went back to him in early March and said, 'You know, I'm really optimistic we're going to meet the targets. The enrollment is going well. The site is working well.'"

Overall, Sebelius contended, the law has been a success. "There are a lot of underlying pieces which really, to me, are very exciting, which go to beginning to fix the underlying health system that affects us all," she said.

Democrats appearing on the Sunday news shows praised Sebelius. In the face of "opposition from the Republicans, she was still able to achieve the 7.5 million goal," said Rep. Elijah Cummings (D-Md.) on CBS's "Face The Nation," referencing the Obama administration hitting its coverage enrollment goal by the end of March.

Sen. Sheldon Whitehouse (D-R.I.) said on "Fox News Sunday" that Sebelius gave "a lot of good service to the president and the country. She was there nearly six years and in an extremely tough job at a very consequential time through the whole health care bill and through the rollout with all these malfunctions. I think it probably is a good thing to have a new face going forward."

Republicans said that Sebelius's departure won't put their worries about the health-care law to rest. "It's not going to quiet the controversy," Rep. Marsha Blackburn (R-Tenn.) told "Face The Nation." "I think it's quite the opposite. What it has done is to elevate some of the concerns."

Burwell was unanimously confirmed by the Senate to head OMB last April. But one Republican cautioned that doesn't mean she will sail through the process for Sebelius's job.

"There's no doubt she was a good choice for OMB," said Sen. Tim Scott (R-S.C.) on "Fox News Sunday." "That does not necessarily make her a good choice for HHS."

Updated at 3:07 p.m.