U.S. Health and Human Services Secretary Kathleen Sebelius is resigning just as the health care law - known as Obamacare - for which she has battled since 2010 appears to have gotten on track after embarrassing early rollout failures, The New York Times reported Thursday.

The newspaper, citing anonymous government sources, said that President Barack Obama has accepted her resignation and on Friday will announce the appointment of Office of Management and Budget chief Sylvia Mathews Burwell to replace her.

The first enrollment period ended just over a week ago for people without health insurance to sign up for it or face a fine under Obamacare. Although the Web site where people could select a health care plan experienced significant and embarrassing technical problems at first, the administration corrected those difficulties and more than 7 million people have now signed up for health insurance.

The 65-year-old former Kansas governor had announced before a Senate committee earlier on Thursday that the number of people who have signed up for private medical insurance under the health care law now stands at 7.5 million, 400,000 more than the figure announced last week by Obama himself.

The New York Times, citing government sources, reported that Sebelius was not forced to resign but rather that her departure from Obama's cabinet was a personal decision, although relations between her and the White House had become more problematic as advisors close to the president had feared that the early Web site problems could seriously mar his presidency.

Although many Republicans have staked out firm positions opposing Obamacare and the party will attempt to make it a central issue in the upcoming mid-term elections, Burwell was unanimously confirmed by the Senate for the OMB leadership post. EFE