Chip Somodevilla / Getty Images Sen. Max Baucus (D-MT) talks with a reporters before attending the weekly Senate Democratic Caucus policy luncheon at the U.S. Capitol November 5, 2013 in Washington, DC.

The Obama administration’s top health care official said Wednesday that problems with the new insurance enrollment website do not threaten the future of the health care reform law, even as a key architect of the law lambasted the roll-out of the Affordable Care Act.

“There’s plenty of time to sign up for the new plans,” Secretary of Health and Human Services Kathleen Sebelius said in testimony before the Senate Finance Committee.

Asked by Montana Democratic Sen. Max Baucus, chairman of the committee, why the administration has not shuttered the troubled Healthcare.gov site until it can be fixed, Sebelius said technical advisers have told her such a wholesale shutdown is not necessary. Baucus, who led passage of the law through Congress and recently warned its implementation would be a “train-wreck,” said Wednesday that the roll-out has been “unacceptable.”

Sebelius appeared before Congress on Wednesday amid sustained Republican calls for her resignation, mass cancellations of insurance policies in the individual market and charges that President Barack Obama misled Americans about how his signature domestic achievement would affect their lives. She testified before the Republican-controlled House Energy and Commerce Committee last week and apologized for the bumpy roll-out of the Affordable Care Act, calling it a “miserably frustrating experience” for consumers.

The secretary took a beating from Republican House members last week and became clearly irritated at times by their questioning. She might have expected to face a friendlier audience before the Democratic-controlled Senate committee on Wednesday. But Baucus’ annoyance and impatience with the administration was palpable.

It’s not an exaggeration to say Baucus wrote the Affordable Care Act. The finance committee’s version of health care reform is closer to the legislation that eventually passed Congress in 2010 than any other version that was debated. As Democratic members of Congress have grown increasingly concerned in recent weeks that implementation of a law they enacted at great political cost has been botched, perhaps no Democrat is more dismayed Baucus.

“I spent two years of my life working on the Affordable Care Act. There is nothing I want more than for it to succeed,” Baucus told Sebelius in his opening remarks on Wednesday.

Baucus reminded the health secretary that he had warned ahead of time that if implementation did not go smoothly, the viability of the new health insurance exchanges, a centerpiece of the law, could be imperiled. And indeed this is the worry of health policy experts who support the law. The dysfunction of Healthcare.gov, the federal exchange web site responsible for enrollment in 36 states, has been hobbled by faulty computer code. Administration officials say it will be fixed by the end of the month, in time for Americans in the individual market to purchase policies by Dec. 15 for coverage that begins Jan. 1.

But Sebelius and her team at HHS promised the Senate Finance Committee and other congressional panels before Healthcare.gov launched on Oct. 1 that it was ready for prime-time.

“Speaking for myself, I want this to work,” Baucus told Sebelius on Wednesday. “I want to do what I can to help you make it work, but it’s a two-way street. You’ve got to tell us what’s going on — candidly, fully — so we don’t wake up at the end of November and low and behold, still nothing yet.”