BILOXI, Miss.  The nation’s governors, Democrats as well as Republicans, voiced deep concern Sunday about the shape of the health care plan emerging from Congress, fearing that Washington was about to hand them expensive new Medicaid obligations without money to pay for them.

The role of the states in a restructured health care system dominated the summer meeting of the National Governors Association here this weekend  with bipartisan animosity voiced against the plan during a closed-door luncheon on Saturday and in a private meeting on Sunday with the health and human services secretary, Kathleen Sebelius.

“I think the governors would all agree that what we don’t want from the federal government is unfunded mandates,” said Gov. Jim Douglas of Vermont, a Republican, the group’s incoming chairman. “We can’t have the Congress impose requirements that we are forced to absorb beyond our capacity to do so.”

The governors’ backlash creates yet another health care headache for the Obama administration, which has tried to recruit state leaders to pressure members of Congress to wrap up their fitful negotiations. Both Ms. Sebelius, who was Kansas’ governor before she joined the cabinet in April, and the federal Medicaid chief, Cindy Mann, made appearances at the meeting on Sunday. Meanwhile, other administration officials spent the day pushing President Obama’s proposal on television talk shows.