DES MOINES, Iowa – Governors came together yesterday on sweeping Medicaid changes that could help President Bush’s budget goals, even as more than a dozen of the chief executives are weighing a legal fight over new Medicare policy that will cost states hundreds of millions of dollars.

The focus at the governors’ summer meeting on the two huge, government-paid health care programs – Medicare for the elderly, Medicaid for the poor – underscored their widespread view that health care is their most urgent issue, for constituents and for states’ financial future.

“This is coming down the pike at us real quick,” Democrat Mark Warner of Virginia said about the complex new policy changes, which governors say will unfairly force them to pay part of Mr. Bush’s new prescription drug benefit. “In January it’s going to be on our doorstep.”

Governors yesterday also stepped up their campaign to improve high school education, agreeing to standardize the way they track graduation rates. National reports last week added fuel to their work, showing high school students hadn’t shown the same gains as younger students.

But worries about Medicare, and the consensus on Medicaid after six months of negotiations among governors, dominated private discussions, most governors said.

Their concerns about Medicare centered on a relatively small portion of Mr. Bush’s huge new drug prescription policy that would affect elderly who are poor enough to qualify for Medicaid and old enough to qualify for Medicare.

Governors have long argued that the federal government should pay the costs of that group, which are significantly higher for each person than for the rest of the Medicaid population.

The new Medicare law takes over paying for those drugs, but requires states to pay the federal government for the overwhelming majority of the bill. Many governors said the complex and cumbersome federal formula means they would pay more money than before, and that state cost-savings were being ignored.

“We’re all talking to our attorneys general and contemplating a suit,” said Democrat Jennifer Granholm of Michigan. “There are about 17 governors who are exploring all possible options.”

She and others said they still hope to negotiate a solution, but several states already have taken more concrete action.

Texas Republican Rick Perry vetoed the entire $444 million that was to go to the federal government for the drug benefits for the next two years, and wrote a letter to fellow governors arguing they should work together to change the federal policy.

In New Hampshire, Democrat John Lynch and state lawmakers took $43 million the state would owe over two years and put it aside until the dispute is settled. “I’m going to talk with other governors to see if there’s some concerted effort we can take,” Mr. Lynch said.

Governors met privately yesterday with Senator Grassley, the Iowa Republican who chairs the Senate Finance Committee that is considering Mr. Bush’s budget goal of reducing the growth of Medicaid by $10 billion over the next five years.

Governors said they all support a proposal to alter Medicaid in hopes of slowing its growing cost, and to give states the chance to experiment with more effective ways to deliver health care.

An Iowa experiment, for example, aims to encourage preventive care by using co-pays to encourage people to make healthier choices. Patients would skip a co-pay if they quit smoking, or lose weight. Those who don’t follow through would be required to pay.

If accepted in Washington, the governors’ plan would allow states to demand co-payments from poor, disabled, and women with children, and add tools to curb seniors from giving relatives their assets so they could get Medicaid-funded long-term care.

Worries from health care advocates have some governors, particularly Democrats, warning that opening the door to co-pays must be accompanied by limits that don’t drive the poorest recipients off government-provided health insurance.

“It’s ill-advised to increase cost-sharing because what it will do is merely have people covered on paper,” said Ron Pollack in Washington with Families USA, a health care advocacy group. “But in reality, they won’t truly have health coverage because they can’t afford it.”

Some governors said that, regardless of what the governors’ association or Congress agrees upon, they won’t pursue co-pays or targeting seniors.

“There’s a moral component to a budget. What do those numbers do, how do they help people?” said Rod Blagojevich, an Illinois Democrat who did not attend the convention. He said he likes the flexibility the NGA plan proposes, but not raising costs for poor and working families.