President Obama sought to defuse criticism of the new health-care overhaul Monday by saying he is willing to give states an earlier opportunity to opt out of certain key requirements – but only if they can find their own ways to accomplish the law’s goals.

The announcement was met with skepticism by many Republican governors who said they need to learn more about it.

“The devil’s in the details,” said Mississippi Gov. Haley Barbour, who is appearing on Capitol Hill Tuesday morning along with Massachusetts Gov. Deval Patrick (D) for a previously scheduled hearing on complying with Medicaid eligibility under the new health-care law.

The 9:45 a.m. hearing before the House Energy and Commerce Committee could provide the first opportunity for lawmakers to elicit feedback on Obama’s announcement.

If Congress approves a change along the lines of what Obama offered, states could gain exemption by 2014 rather than 2017 from some central and controversial elements of the law: that most Americans carry health insurance, that many employers offer their workers coverage, and that states create insurance marketplaces to help individuals and small businesses buy health plans that meet federal rules.

To win that freedom, though, Obama reminded the governors at a White House meeting that states would have to prove to federal officials that they could still achieve the law’s objectives. Specifically, they would need to demonstrate that insurance benefits would be as affordable and as comprehensive, that the same number of residents would gain coverage, and that the alternate approach would not deepen the federal deficit.

With a majority of states trying to overturn the law in the federal courts and Republican governors complaining that it gives federal regulators too heavy a hand, the president sought to move the debate onto new ground by forcing the law’s critics to prove that their vision for the nation’s health-care system could work.

“Many of these states contend they can do more with less if they get the flexibility to be more creative,” said Drew Altman, president of the Kaiser Family Foundation, a nonpartisan health policy group. “This puts the onus back on them and calls that into question.”

In taking this new tack, the White House is endorsing a proposal introduced late last year by a bipartisan trio of senators. The bill, sponsored by Sens. Ron Wyden (D-Ore.), Scott Brown (R-Mass.) and Mary Landrieu (D-La.), would accelerate a provision in the law that would allow states to ask federal health officials for “innovation waivers” starting in 2017 that would free them to devise ways to improve health care. The legislation would move up the date to 2014.

The change in timing is significant, because 2014 is when the provisions in question are to go into effect, so states could – in theory, at least – get permission early enough to avoid the requirements.

“I think that’s a reasonable proposal. I support it,” Obama told the governors who convened at the White House on Monday as part of the National Governors Association’s semi-annual meetings. “It will give you more flexibility more quickly, while still guaranteeing the American people reform. If your state can create a plan that covers as many people as affordably and comprehensively as the Affordable Care Act does – without increasing the deficit – you can implement that plan. And we’ll work with you to do it.”

Although the president has endorsed the idea, Congress would still have to approve the change for states to get relief by 2014. If it did, Health and Human Services officials would then need to write rules defining specifically how states could meet criteria for a waiver.

The immediate reaction – among the governors and on Capitol Hill – was mixed.

The governors said Obama’s willingness to release them earlier from some of the law’s requirements was welcome. But most stopped short of embracing the idea fully, with Republicans sounding especially wary.

“A number of our fellow governors would be very interested in supporting this,” said Washington Gov. Chris Gregoire (D), the NGA’s chairman. “We need to talk to them to see if we can put our support behind that bill as the National Governors Association.”

Kansas Gov. Sam Brownback, who opposed the health-care legislation as a member of the Senate, said Obama’s proposal doesn’t negate what he and other Republicans consider a fatally flawed law that they will continue to challenge in the courts. “This offers a little bit of flexibility, which I think is a positive thing,” he said, “but it doesn’t change the overall objection to the bill.”

Other Republicans were equally cautious. Sen. Orrin G. Hatch (Utah) called Obama’s new timetable a “gimmick” that would not provide genuine relief.

Governors’ more immediate focus was on the potentially crushing burden of rising Medicaid costs. Gregoire said the NGA would accept the president’s challenge to develop a bipartisan set of recommendations that would give states more flexibility to curb Medicaid spending. But Republicans, some of whom favor converting the health insurance system for the poor from an entitlement program to a block grant, remained skeptical that Obama will authorize real changes. New Jersey Gov. Chris Christie said that on the question of Medicaid flexibility, the president “said some very nice things and he says them really nicely.” But, he added, “I didn’t hear any real substance” that would suggest the governors will get what they want.

The proposal to give states greater freedom from the health-care law would not specifically allow governors to deviate from Medicaid’s rules for who must be covered and what medical services they must be able to receive. The proposal would, however, let states send HHS officials a combined request to alter Medicaid and their approach to health-care reform.

On Capitol Hill, a spokesman for Senate Majority Leader Harry M. Reid (D-Nev.) said: “The date was set at 2017 because that was the earliest experts thought these measures could be implemented, but we are open to hearing the administration’s reasons for concluding that they can be implemented earlier.”

Mike Leavitt, a former Utah governor, called Obama’s announcement “sort of a hollow victory.” Leavitt, who was a major proponent of state experimentation with health care when he led the Department of Health and Human Services under President George W. Bush, said that Obama was essentially telling states, ” ‘We’ll give you permission to ask for permission sooner rather than later.’ What Republicans are saying is that we don’t want to have to ask for permission at all, because we can’t afford to build the system that you’ve laid out for us.”

An aide to Wyden, a liberal who also has long favored giving states more freedom to devise their own health-care approaches, said that officials from the White House and HHS have been conferring with the senator since shortly after he and Brown introduced the legislation in late November.

“It was a process of persuasion,” the aide said. “They’ve been coming around for a while and just kind of came to fruition recently.” So far, the aide added, Oregon, Vermont and Massachusetts – which developed its own health exchange before the federal law was enacted – are the only states that have said they will pursue a waiver.

goldsteina@washpost.com balzd@washpost.com

Staff writers N.C. Aizenman and Perry Bacon Jr. contributed