BILOXI, MISS. --  Democratic governors on Monday softened their opposition to health care legislation being championed by Democrats in Washington after accusing staff at the National Governors Association meeting of misleading them on the costs of the reforms.

The majority who gathered at the National Governors Association meeting this weekend had publicly agreed with their GOP colleagues that the health care bill would turn into unfunded mandates and would squeeze their already depleted state budgets. 

But after meeting for an hour Sunday night with Health and Human Services Secretary Kathleen Sebelius, several Democratic governors accused NGA staff of misleading them on the cost of the bill.

"Yesterday the NGA staff gave us some information that was not exactly correct so we're working through to find out what the real numbers are," Montana Gov. Brian Schweitzer told FOX News on Monday. "Currently the House version does not shift any liability to the states. If that's the version that's ultimately passed, well be happy with it." 

"Once Kathleen Sebelius talked with the governors we came to understand that we were given bad information by NGA staff," added Maryland Gov. Martin O'Malley.

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O'Malley said that according to the House bill, "The federal government has not shifted cost. The federal government is taking care of its obligations. Which was really good news for the governors. Whatever fears were around this place because of bad information we got from the NGA, that's greatly dissipated."

NGA staff did not respond to a request for comment on the accusation aides had misled the chief executives.

Despite Sebelius' alleviating some of the governors' concerns, others said her description relies only on the bill in the House of Representatives, and they remain wary of the final outcome once it leaves the Senate.

"That's the message that is being sent: Please work within the House frame of Congress being able to take care of that within the confines of the federal budget and not putting it on the back of state budgets," said Gov. Joe Manchin of West Virginia, who was named the new vice chairman of the NGA during the four-day conference that wraps up on Monday.

"We're concerned that there might be other mandates coming down," Manchin said.