Updated

BILOXI, Miss. -- On the third day of their annual meeting, governors from both parties raised concerns over a health care bill being pushed by Democrats in Washington, D.C.

In a heated closed-door session, both Republican and Democratic governors criticized the bill that many said could turn into another unfunded mandate from Congress. The issue dominated the afternoon discussion.

"The governors are concerned about unfunded mandates, another situation where the Federal government says you must do X and you must pay for it. Well if they want to reform health care, they should figure out what the rules are and how they are going to pay for it," Democratic Montana Gov. Brian Schweitzer told FOX News.

"Instead what they are proposing is -- they're figuring out the rules and forcing the states to pay for it," he said.

A major worry for many governors is potential cost increases that would fall on states in order to expand Medicaid programs.

"This huge expansion of Medicaid would be extremely expensive in my state. We anticipate that it would increase spending on Medicaid by 50 percent, and that's money we don't have. And other states don't have it either," Gov. Haley Barbour, R-Miss., head of the Republican governors, said after the mid-day meeting.

The new chairman of the National Governors Association, Vermont Republican Jim Douglas said that while many governors want to re-vamp the health care system, they feel the bill's current structure unfairly burdens the states at a time when their budgets are already stretched thin.

"Our concern as governors is Congress not impose a cost that we can't absorb at a time when our budgets are under tremendous stress," Gov. Douglas told FOX News.

"I don't know what the pace might be but we're going to keep resisting an unfunded mandate from Washington," he said.

The governors conclude their meeting on Monday.