WASHINGTON (AP) — Anxious to ease deepening political tensions with the states, President Barack Obama on Monday told governors he wants to speed up their ability to enforce his signature health care law on their own terms. But his concession goes only so far: He warned he won’t allow states to weaken the law.

He also told them not to vilify their own states’ public workers while struggling with spending cuts.

Hosting governors of both parties on his own turf, Obama offered them what they often request: more flexibility as they cope with painful budget dilemmas. Declaring that he would “go to bat for whatever works,” Obama supported letting states propose their own health care plans by 2014 — three years faster than the current law allows.

Yet this would be no change to the fundamental requirements of a federal law that has divided the nation and prompted about half the states to try to overturn it through lawsuits. To gain new powers, states would first have to convince Washington that their plans would cover as many people, provide equally affordable and comprehensive care and not add to the federal deficit.

More broadly, Obama sought to send a message — both cooperative and pointed — as leaders at all levels of government grapple with huge economic pressures. The yearly gathering of the president and the state chief executives came as budget disputes are roiling, most notably in Wisconsin, where dramatic protests have raged for days.

Calling for shared sacrifice, Obama said public workers understand they must absorb their share of budget cuts. But he delivered a sharp message to governors seeking to strip away union protections, saying: “I don’t think it does anybody any good when public employees are denigrated or vilified, or their rights are infringed upon.”

Wisconsin’s governor, Scott Walker, was not at the White House but rather in his home state as a nationally watched budget showdown rolled on. He called for Democratic lawmakers to return to the state by Tuesday and vote on his bill that would end most collective bargaining rights for public employees as part of a plan to plug a $3.6 billion shortfall.

Republican governors generally gave a thumbs-down to Obama’s pledges of flexibility on the health care law, which requires Americans to buy health insurance or pay a penalty beginning in 2014.

“I was disappointed,” said Texas Gov. Rick Perry, chairman of the Republican Governors Association. “Pretty much all he did was reset the clock on what many of us consider a ticking time bomb” that could “crush our budgets.”

The GOP governors’ group is airing TV and radio ads in Wisconsin supporting Walker and criticizing Democratic state senators who have relocated to Illinois to block enactment of his agenda.

“Oklahoma wants to do Oklahoma’s own plan,” said that state’s Republican governor, Mary Fallin. Asked whether Obama’s plan was flexible enough, she said: “We’ll see.”

The closer Republicans look at the details, the less flexibility they will see, said economist Douglas Holtz-Eakin, leading domestic policy adviser to 2008 GOP presidential candidate John McCain. “If you can’t control eligibility or the benefits package, it’s like saying: ‘Here’s the bill, you go figure out how to pay for it,'” he said.

Michael Steel, spokesman for House Speaker John Boehner, R-Ohio, said Obama’s offer has no more flexibility. “It’s a head fake,” said Steel.

White House officials said the administration was not backing away from the individual coverage requirement, but that the provision, ultimately, is only a means to an end. If states can show they’ll achieve the same goals through a different approach, the administration is willing to sign off. White House officials said they still believe the individual mandate is the best way to meet the law’s coverage and affordability targets.

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,” the president said. “I support it.”

Republican governors control most of the 26 states that have sued to stop Obama’s health care overhaul, his signature domestic accomplishment. They say it would cost their states too much money. Court rulings so far have been mixed, upholding the law more times than not. Last month in Florida, U.S. District Judge Roger Vinson ruled the law was unconstitutional.

During the state executives’ closed session with Obama, South Carolina Gov. Nikki Haley said she told the president that 29 governors were seeking an expedited Supreme Court handling of the federal health care law challenge, following the Florida decision. “We’ve got to get answers for these governors,” Haley said in an interview with The Associated Press.

For his part, Obama showed no give on the law’s core elements. He said was convinced the law would cut costs, end insurance industry abuses and “cover everybody.”

“I am not open to refighting the battles of the last two years or undoing the progress that we’ve made,” Obama told the governors when reporters were in the room. “But I am willing to work with anyone, anybody in this room, Democrat or Republican … to make this law even better.”

Over the next two-and-a-half years, states face an estimated $175 billion more in budget gaps that they have no choice but to fill. Unlike the federal government, states are required to balance their budgets. Their upcoming problems will be caused partly by the loss of money as the nation’s 2009 emergency economic stimulus law, or recovery act, dries up.

Obama noted that point and sympathized with the states’ budget crunch. Here, too, though, Obama took the governors to task for those who have criticized the costly stimulus law.

“It is undeniable that the recovery act helped every single state represented in this room manage your budgets,” he said, “whether you admit it or not.”

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Associated Press writers Ricardo Alonso-Zaldivar, Philip Elliott, Julie Pace and Liz Sidoti in Washington and Jim Davenport in Columbia, S.C., contributed to this report.