Washington ? Two governors appear to lead the pack when it comes to heading the Health and Human Services Department for President Barack Obama.

One of those governors is already under attack. The other was seen Thursday night meeting at the Ritz Carlton with Obama’s senior adviser.

The pick of Tennessee Gov. Phil Bredesen would clearly cause Obama problems with some of the advocacy groups calling for a health care overhaul this year. One of those groups, Health Care for America Now, put out a statement Friday saying it “couldn’t think of anyone more wrong for health care reform or more wrong for America.”

The advocacy groups have battled Bredesen over the years for his efforts to cut spending in the state’s TennCare program, which provides health care for the poor.

The other governor much discussed as HHS secretary is Kathleen Sebelius of Kansas. Sebelius was in town to deliver two speeches, one on Thursday at a conference on clean energy jobs, and one Friday at the National Education Association. In between, she managed to meet with Valerie Jarrett, a senior adviser to Obama.

A White House aide said no decision has been made concerning who will be the next HHS secretary, but officials were working quickly.

“President Obama has made it clear that reforming our broken health care system is a top priority, and he’s moving swiftly to nominate a partner in carrying out that mission,” said aide Reid Cherlin.

Gov. Sebelius’ spokeswoman, Beth Martino, confirmed the meeting with Jarrett but said she didn’t know what they talked about: “She had a meeting with her friend Valerie Jarrett, whom she has known for several years.”

The trip by Sebelius was planned in advance of former Senate Minority Leader Tom Daschle, of South Dakota, bowing out as nominee for HHS secretary as a result of fallout from about $140,000 in back taxes and interest he paid last month.

Sebelius is a two-term governor who campaigned often for Obama. Advocacy groups like the consumer watchdog role she played as insurance commissioner for eight years before she became governor.

Her name had been floated for several Cabinet posts, but she announced in early December that she had removed herself from consideration from a Cabinet job, citing Kansas’ budget problems that needed her attention.