WASHINGTON – After meeting with President Bush, governors expressed concern yesterday that the administration’s proposal to cut some $40 billion from the Medicaid health insurance program for the poor would further strain already tight state budgets.

“All governors are very, very reluctant to see any kind of major reduction to the system,” said Bob Riley, a Republican of Alabama.

Democrat Janet Napolitano of Arizona said the president was too focused on a specific figure that would help reduce the federal deficit. “If the president wants Medicaid reform, then he needs to have a reform discussion that’s not driven by an arbitrary budget number,” she said.

Some governors, however, said they realized they eventually must compromise. They also wanted the ability to experiment in order to lower costs. Many were encouraged by parts of the administration’s budget proposal that would give states more flexibility.

At the meeting, Mr. Bush promised to work with governors to restrain soaring Medicaid costs and revamp the program. But he also indicated he would keep trying to eliminate some federal aid.

“We want Medicaid to work,” Mr. Bush told the governors before an hour-long, private question-and-answer session. “The system needs to be reformed and we want to work with governors.”

But the one detail Mr. Bush emphasized was his plan to cut federal dollars in an effort to stop state Medicaid accounting practices that the administration contends cheat taxpayers.

Many state leaders say the money derived this way is essential. Federal officials say the practice artificially inflates health care prices to bring in more federal cash, which states sometimes use for other purposes.

“We’re worried” about the transfers, Mr. Bush said. “We put that on the table for discussion, so that the system works the way it’s supposed to work.”

Mr. Riley said Mr. Bush’s proposed cuts would cost Alabama $150 million over the next four or five years. Meanwhile, the number of Alabama residents on Medicaid has climbed from one in 10 to nearly one in five. Cuts will mean fewer services and probably force people off the rolls, Mr. Riley said.

Medicaid costs have soared in recent years, driven by rising health care costs, an aging population that relies largely on Medicaid to pay for nursing homes, and a recession that sent more people to state-supported health care.

This year, Medicaid will pay to care for 53 million people – women and children, poor, elderly, disabled. It will cost an estimated $329 billion. Enrollment has increased by 40% over the past five years.

A group of governors has spent the past month hoping to develop a plan to present to the administration and Congress that would counter Mr. Bush’s cuts with changes that would save money without hurting state budgets.

A deal, either among governors or in discussions between them and Health and Human Services Secretary Mike Leavitt, has proved elusive.

Governors said Mr. Bush was encouraging; though Republicans were more welcoming of the administration’s stance than Democrats, partisan lines did not define them. There were signs that governors recognized the need for compromise. “There’s opposition to any reduction but we have to be realistic,” said Bill Richardson, a Democrat of New Mexico.

“It’s not about this week,” said Mark Warner of Virginia, a Democrat. “Getting it right is more important than getting it quick.” Mr. Warner said the struggle over the final budget numbers will rest with Congress.

Even the impact of the budget was in dispute. Governors complained of $60 billion in cuts over 10 years. But the administration, and the National Governors Association analysis, said reductions were offset by additional spending, leaving the cut at about $40 billion.

Governors from all sides of the political spectrum say now is the time for a significant re-examination of Medicaid. But what that means has not become clear.

Mr. Bush’s budget would make it more difficult for older people to transfer their assets to family members so they qualify for Medicaid coverage for nursing home care, one of the large cost-drivers of the system. The president’s spending plan also would affect an effort to lower drug prices, which several governors said showed promise.