Health and Human Services Secretary Kathleen Sebelius somewhat inartfully rejected the onslaught of demands, leveled most prominently by Republican lawmakers, for her to resign over the botched rollout of the new Obamacare website.

"The majority of people calling for me to resign, I would say, are people who I don't work for and who do not want this program to work in the first place," Sebelius said Thursday during an appearance at a Phoenix Health and Human Services call center. "I have had frequent conversations with the president, and I have committed to him that my role is to get the program up and running and we will do just that."

When asked if any heads have rolled in the administration over the problem-plagued website, she responded, "No one - no one has been fired."

Republicans pounced. "It is amazing that the Obama administration doesn't understand that their bosses are the American people. Maybe that is why the administration continues to push this train wreck of a healthcare law and refused to heed years of warning signs that Obamacare was the wrong prescription to fix America's healthcare problems," Reince Priebus, chairman of the Republican National Committee, said. "It's time for President Obama to do what he should have done weeks ago and fire Secretary Sebelius."

HHS issued a clarification Friday, saying the secretary's remarks were "aimed at reminding people of the longstanding political opposition to the law."

"The secretary serves at the pleasure of the president and for the American people, many of whom desperately need affordable health care. She is committed to getting this right and ensuring that HealthCare.gov is working smoothly," spokeswoman Joanne Peters said.

Sebelius' comments came on the same day that several dozen members of Congress - all Republicans - sent a letter to President Obama urging him to fire Sebelius.

"By calling for the resignation of Secretary Sebelius, you can send a powerful signal that the American people will not be held responsible for her department's failures," the lawmakers wrote Thursday.

The White House continues to stand by the secretary and says she has the full confidence of the president.