A growing number of Republican state leaders are revolting against the major Medicaid expansion called for under President Obama’s health-care overhaul, threatening to undermine one of the law’s most fundamental goals: insuring millions of poor Americans.

The Supreme Court opened the door Thursday when it announced that although the rest of the law is constitutional, the federal government cannot punish states that refuse to adopt the measure’s more generous eligibility rules for Medicaid.

The Republican governors of four states — Florida, Iowa, Louisiana and South Carolina — have declared that they want to opt out of the expansion. Leaders of half a dozen other states — including Texas, home to one of the largest concentrations of uninsured people — are considering following suit.

The governors argue that expanding their Medicaid programs, which are jointly funded with state and federal money, would crush state budgets. And they are turning the issue into a roiling election-year battle over the federal government’s role.

“The president . . . needs to understand what makes this country great in part is that we’re not dependent on government programs,” Louisiana Gov. Bobby Jindal said Tuesday on Fox News Channel’s “Fox and Friends” program. “It seems to me like the president measures success by how many people are on food-stamp rolls and government-run health care. That’s not the American Dream.”

Such a message has the potential to further fuel the tea party movement, which galvanized three years ago over the health-care legislation and could put enormous pressure on GOP leaders. Already, large tea party organizations such as Americans for Prosperity and FreedomWorks are urging their members to lobby states to reject the federal Medicaid money, with a particular focus on the 27 that challenged the law in court.

The ramifications could be far-reaching, because the law’s top ambition is to extend coverage to 30 million uninsured Americans. More than half of those people are slated to receive insurance through the Medicaid expansion.

“This has always been the core of the law, and the court has just made it optional,” said Matt Salo, director of the National Association of Medicaid Directors.

The prospect has alarmed and energized not just advocates for the poor but also representatives of hospitals, which are chronically burdened with the cost of treating the uninsured. Hospital associations agreed to help fund the law by accepting various cuts to their reimbursement rates with the expectation that they would be more than compensated by money from patients newly insured through Medicaid.

Now they worry that they will be stuck with only the downside of that bargain, said Bruce Rueben, president of the Florida Hospital Association.

“If you’re dealing with a high number of uninsured people and your payments from other sources go down, you have no way to cover that unmet cost,” he said.

Salo predicted that hospital representatives will soon be directing a lobbying blitz at governors and state legislatures — which, in most cases, will decide whether to expand Medicaid.

“They are going to be camping out at the doorstep. And they will do that in all 50 states,” he said.

White House officials contend that this is only one of several reasons the vast majority of states will eventually go along with the Medicaid expansion — which, beginning in 2014, will open the program to people with incomes at 133 percent of the federal poverty level, a far more generous standard than what most states currently offer.

On ABC’s “This Week” on Sunday, White House Chief of Staff Jacob J. Lew noted that the government will pay the full cost of covering the newly insured in the first three years, and never less than 90 percent after that.

“It is the most generous federal match in the history of Medicaid,” he said. “And I think a governor’s going to have to answer to their own people. . . . For those few that are slow to come in, they’re going to have to answer to people why they’re turning this down and why they’re letting people go without coverage.”

Republicans counter that the state share of the tab could still prove crippling. And the argument offers a chance to hammer home a major GOP talking point: that the government cannot keep growing without fraying at the seams, said Rich Galen, a Republican strategist who served as press secretary for then-House Speaker Newt Gingrich (Ga.).

“The issue is: If you keep expanding unemployment insurance and expanding Medicaid and expanding food stamps, then sooner or later the money runs out and you become Greece or Spain or Italy,” Galen said. “They’re not saying, ‘I want people dying in the streets.’ They’re saying they want to fix the economic infrastructure.”

Several analysts suggested that governors could be playing for leverage to gain more flexibility to shape their Medicaid programs in the event that Obama is reelected.

“It’s a fantastic negotiating strategy,” said Robert Laszewski, a health-care consultant and former insurance executive.

He predicted that governors could push Obama for permission to privatize parts of their Medicaid programs or to open eligibility only to those with incomes up to 100 percent of the poverty level instead of 133 percent. They also could request that the federal contribution to Medicaid be sent to them as a block grant without strings attached.

“I think they’re going to work themselves a much better deal than they would have had and then declare a Republican victory, because they’re essentially going to get some form of Republican Medicaid reform,” Laszewski said.

Still, Wisconsin Gov. Scott Walker (R) is one of several who said they are waiting for the November presidential election in hopes that a victory by Mitt Romney could empower the GOP to repeal the overhaul.

And if the law survives the election, would Walker favor expanding his state’s Medicaid program? “It’s premature to comment on that,” said his spokesman, Cullen Werwie.