WASHINGTON - Offering to be more flexible on implementing the health-care law, President Obama called Monday for letting states move sooner to develop alternative plans for meeting its goals - including expanding insurance coverage.

While maintaining his insistence on achieving the law's aims, Obama said he was willing to allow governors to propose their own strategies as early as 2014 - instead of waiting until 2017 as the current law provides.

"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," he told governors gathered at the White House. "And we'll work with you to do it."

The existing law, passed last year, allows states, starting in 2017, to seek waivers from requirements such as the mandate that all Americans get health insurance, as long as the states showed that their alternatives would deliver the same benefits - for consumers and for the budget.

Obama's offer - which drew swift criticism from several Republican officials - underscored the intensifying cat-and-mouse game that the administration is playing with Republicans over health care as the 2012 presidential election cycle begins.

Republican officials nationwide are stepping up their criticism that the law does not give states enough freedom to design their own solutions to the health-care crisis.

The GOP now controls 29 governorships, up from 23 last year. Most of the states they govern, including Pennsylvania, have joined lawsuits challenging the health overhaul's constitutionality.

Responding to the new political reality, the Obama administration has begun highlighting its responsiveness to state needs without yielding on the basic elements of Obama's signature domestic-policy achievement.

"I am not open to refighting the battles of the last two years, or undoing the progress that we've made," Obama warned his critics Monday.

The law already gives states substantial authority to design their own systems, including setting up and regulating their own insurance markets.

Under the proposal Obama endorsed, which must be approved by Congress, states might design a program that would expand coverage for lower-income people using private health insurance instead of relying heavily on the government Medicaid program, as the health-care law does.

Or it might allow a state to develop an alternative to the controversial individual mandate that will penalize Americans who do not get insurance starting in 2014. Other countries use different mechanisms to encourage healthy people to buy insurance.

It might even allow some traditionally liberal states, such as Vermont, to explore single-payer systems for expanding coverage.

"The president is serving it up to the governors on a plate," said Sen. Ron Wyden (D., Ore.), who coauthored the waiver proposal with Sen. Scott Brown (R., Mass.).

J. Fred Ralston Jr., president of the American College of Physicians, expressed hope that the proposal "could provide a basis for much-needed bipartisanship."

States would not be able to eliminate consumer protections in the law, such as the requirement that insurers offer coverage to people regardless of their health.

And states would still have to guarantee that insurers offer a minimum set of benefits to be set by the federal government, another key requirement of the new law.

It remains unclear how many states would seek such waivers, or if Republicans on Capitol Hill would even back legislation to give states the option.

GOP governors are already pressing the administration for permission to cut some people off Medicaid, saying they cannot afford to maintain current coverage levels.

Health and Human Services Secretary Kathleen Sebelius has approved a request from Arizona to pare back its program. And the administration is offering help to other states as they look for ways to hold together their budgets as they struggle with providing health care to millions of unemployed workers.

But Republican officials - who continue to push for a full repeal of the 2010 law - have dismissed many of these overtures and called Obama's new offer a publicity stunt.

"I was disappointed," Texas Gov. Rick Perry said. "Pretty much all he did was reset the clock on what many of us consider to be a ticking time bomb that is absolutely going to crush our state budgets."

In announcing the offer Monday, Obama also tweaked former Massachusetts Gov. Mitt Romney, one of his potential Republican presidential rivals.

"I agree with Mitt Romney, who recently said he's proud of what he accomplished on health care in Massachusetts and supports giving states the power to determine their own health-care solutions," Obama said. "He's right."

The Massachusetts law that Romney enacted, which is a model for the federal law, is considered one of Romney's major liabilities as Republicans appeal to conservative activists who will dominate the primary elections. Other Republicans have called for repealing the federal law.

Also Monday, the administration said in court papers that a judge in Virginia erred in striking down the law's centerpiece. It urged a federal appeals court to reverse the ruling, arguing that the requirement that citizens buy insurance or pay a penalty starting in 2014 is allowable under the Constitution's Commerce Clause.

This article includes information from the Associated Press.