Addressing the nation's governors, Obama also challenged state chiefs who have sought to balance their budgets through weakening unions and curbing employees' benefits, telling them that they should not demonize workers.
"I don't think it does anybody any good when public employees are denigrated or vilified or their rights are infringed upon. We need to attract the best and the brightest to public service," the president said.
About half the states are suing to overturn Obama's health care law, targeting its unpopular requirement that most Americans carry health insurance or face fines from the IRS. Obama told the governors that if any of them have better ideas, they're welcome to propose it and see if it works.
First they would have to convince Washington that their approach covers at least as many state residents, provides equally affordable and comprehensive benefits, and would not increase the federal deficit.
"If your state can create a plan that can cover 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," Obama told the governors.
Obama's offer is not as sweeping as it may sound at first. In fact, the law already allows states to propose their own framework for health care. But under the law, states cannot offer their plans until 2017. The president said Monday states could submit their ideas three years earlier, in 2014.
Liberal-leaning states like Vermont would be able to experiment with a coverage-for-all approach similar to Medicare while Republican-leaning states would be able to propose plans that don't rely on a government mandate to buy insurance. One alternative would be to automatically enroll people in health coverage.
The idea to move up the date for state experimentation did not start with Obama. Democratic Sen. Ron Wyden of Oregon and Massachusetts Republican Sen. Scott Brown have already proposed it in legislation. But the president gave it a prominent endorsement.
"I think that's a reasonable proposal, I support it," Obama said Monday. "It will give you flexibility more quickly, while still guaranteeing the American people reform."
The health care law's big push to cover the uninsured won't come for another three years. Starting in 2014, many middle-class households will be able to buy taxpayer-subsidized private coverage through new state based insurance markets. And more low-income people would be signed up for Medicaid. The law will expand coverage to more than 30 million now uninsured.
But Obama didn't just offer compromise to Republican governors. He challenged state chiefs over their treatment of unions.
Obama said all stakeholders must have a role in discussions about state budgets and employees should not lose rights as governors look to cut spending. His comments come as Republican governors in Wisconsin and Ohio back bills that would end collective bargaining agreements for public employees.
Obama said he understands the fiscal challenges facing cash-strapped states and says everyone should be prepared "to give something up."
"We're not going to attract the best teachers for our kids, for example, if they make only a fraction of what other professionals make," Obama said. "You're not going to convince the bravest Americans to put their lives on the line as police officers or fire fighters if you don't properly reward their bravery."
Associated Press writers Julie Pace and Philip Elliott contributed to this report.