Health and Human Services Secretary Kathleen Sebelius said Wednesday that the government is working to fix a “couple of hundred” problems with the federal health insurance Web site and that once the site is running smoothly, she will “re-invite” people who have been turned off by the technical headaches.

Sebelius, appearing before the Senate Finance Committee, rejected calls from politicians in both parties to delay aspects of the health-care law, including by extending the initial open enrollment period beyond March 31 for buying insurance on the new online marketplaces. People who don’t buy coverage by then risk being fined.

“There’s plenty of time to sign up for the new plan,” she said.

Her testimony came as President Obama renewed the administration’s pledge that the site will be fixed by the end of the month and challenged Texas Gov. Rick Perry (R) to use another provision in the law to expand Medicaid to nearly 1 million state residents.

“One thing that gets me frustrated is folks complaining that the Web site is not working. ‘Why is Obama not fixing it?’ Yet they leave a million people without health insurance that they could immediately fix,” the president told several dozen health-care organizers at a temple in Dallas, without mentioning Perry by name.

The White House is expected on Thursday to announce $150 million in grants to establish new community health centers, which would help provide care to more than 1 million people.

The idea of extending the open enrollment period drew increased attention after the insurer Humana raised the idea Wednesday during a conference call with investors. “Our assumption is that there will be an extension to the open enrollment period,” chief operating officer Jim Murray said.

A spokesman later clarified that the company had not received any guidance from the administration, but that it is including the possibility of an extension in its planning.

Insurance-industry officials say extending the sign-up period could increase premiums in 2015.

On Capitol Hill, Sebelius acknowledged that trying to use HealthCare.gov had been a “miserably frustrating” experience for many people, and she took responsibility for the problems. “I recognize that there’s an even higher level of accountability — accountability to the sick, the vulnerable, the struggling Americans who deserve better health care,” she said in her opening statement.

Sen. Max Baucus (D-Mont.), chairman of the committee and an architect of the health-care law, told Sebelius that he was disappointed with the botched rollout, as did Sen. Bill Nelson (D-Fla.), who urged her to come down hard on those who contributed to the problems. “I want you to hold them to account,” he said. “I want you to burn their fingers and make ’em pay for not being responsible and producing a product that all of us could be proud of.”

At the same time, news emerged that the director of the Centers for Medicare and Medicaid Services’ Office of Information Services, which helped develop the Web site, is retiring.

Tony Trenkle is leaving the agency to take a position in the private sector, CMS chief operating officer Michelle Snyder said in an e-mail to colleagues. CMS is part of HHS.

Snyder, who is Trenkle’s boss, and Trenkle’s deputy, Henry Chao, have been mentioned as people who played prominent roles in the rollout of HealthCare.gov. Federal officials and contractors have testified that the site did not undergo sufficient testing before the Oct. 1 launch.

The administration has signaled that it would exempt some labor unions and businesses from a new fee established by the health-care law, according to Kaiser Health News, a nonprofit news service. Unions had complained about the temporary reinsurance tax, which is $63 for each person covered in a health plan. The exemption would be for 2015 and 2016.

Amy Goldstein and David Nakamura contributed to this report.