"We want Medicaid to work," Mr. Bush said after meeting with the governors. "We also recognize that the system needs to be reformed. And we want to work with you to do so," he added.
Governors were optimistic that Mr. Bush was serious about changing the system, but they worried that the cuts would further strain state budgets.
"All governors are very, very reluctant to see any kind of major reduction to the system," Republican Bob Riley of Alabama said.
Democrat Janet Napolitano of Arizona said the president is too focused on a specific figure that will 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.
Before the White House meeting, governors said they opposed Mr. Bush's proposal to cut some $40 billion from the system. 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.
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 cheats taxpayers.
Many state leaders say the money derived this way is essential. Federal officials say it 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."
Riley said the president's proposed cuts would cost Alabama $600 million over the next four years or five years. Meanwhile, the number of Alabamans 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, Riley said.
Medicaid costs has 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 for care for 53 million people — women and children, poor, elderly, disabled. It will cost an estimated $329 billion. Enrollment has increased by 40 percent 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 governors and Health and Human Services Secretary Mike Leavitt, has proved elusive.
"It's not about this week," said Mark Warner of Virginia, a Democrat. "Getting it right is more important than getting it quick." 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.
Democrat Tom Vilsack of Iowa talks about preferred drug lists. Republican James Douglas of Vermont emphasizes keeping people on the Medicaid rolls, but reducing the program's costs. Republican Mark Sanford of South Carolina wants to let patients and their families decide how to spend a set amount of health care dollars.
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 for the fiscal year beginning Oct. 1 also would affect an effort to lower drug prices, which several governors said showed promise, and a change to taxes on providers, which governors said would shift costs to them.
Democrat Phil Bredesen of Tennessee, who met briefly with Leavitt before the White House discussion, said he was encouraged by the administration's overall approach. But he said he was disappointed it the plan did not go further.
"It's not going to transform the system," Bredesen said. The governor knows the stakes: This year, he acted to cut 323,000 people to maintain solvency for his state's expanded Medicaid system, known as TennCare.