WASHINGTON — With two Supreme Court victories in the past three years, Republicans lacking a serious alternative and millions of previously uninsured Americans now in health plans, the Affordable Care Act is about as firmly ensconced as a law can be in a politically divided country.

The court, in a strongly worded 6-3 decision written by Chief Justice John G. Roberts Jr., pushed aside the latest legal challenge that threatened to take away insurance subsidies that more than 6 million Americans rely on to get health care.

In the decision, Roberts explicitly blessed the law’s sweeping system for guaranteeing coverage, noting that the model succeeded where previous attempts had failed.

And although many Republicans kept up their rhetorical attacks in the ruling’s immediate aftermath, the prospects that the GOP would take away coverage from the more than 20 million Americans who have come to rely on the law have all but evaporated.

In Washington, congressional Republicans have no plan to replace the law President Barack Obama signed more than five years ago.

And a growing number of Republican governors are signaling their interest in moving on.

“We appreciate that the deep uncertainty of this issue has been resolved,” Michigan Gov. Rick Snyder said Thursday after the court issued its decision. “The health and well-being of the people of Michigan is always a top priority.”

In his state, more than 200,000 low- and moderate-income residents stood to lose insurance assistance if the court had backed the challengers, who argued that no subsidies should be available in any state that did not establish its own insurance marketplace through the law.

Michigan is one of 34 states that fully rely on the federal HealthCare.gov marketplace.

Snyder, like many Republican governors, is more focused on expanding access to health care for his constituents than the political fight over Obamacare. Michigan is working to secure approval from the Obama administration for further changes to the state’s Medicaid program, which was expanded under the law to guarantee coverage to the state’s poorest residents.

Michigan is one of 29 states that have accepted federal aid through the law to expand Medicaid coverage, a number that has steadily grown over the last several years as even Republican governors accept the permanence of the law.

In Washington and around the country, supporters of the health law redoubled their calls on Republicans to stop fighting the Affordable Care Act.

“Now that the Supreme Court has ruled, instead of trying to undermine the law, opponents of health reform in Congress should accept that health reform is here to stay,” said Sue Berkowitz, head of South Carolina Appleseed, a nonprofit that has been working to expand coverage in that state.

Obama joined the chorus, speaking from the White House after the court ruled Thursday.

“The Affordable Care Act is here to stay,” he insisted.

The president’s remarks will not quell the ongoing political battle over the health law, which Republicans have used to expand their congressional majorities in the two midterm elections.

Indeed, former Florida Gov. Jeb Bush, the front-runner for the 2016 GOP presidential nomination, pledged Thursday to keep up the fight.

“As president of the United States, I would make fixing our broken health care system one of my top priorities,” he said. “I will work with Congress to repeal and replace this flawed law with conservative reforms that empower consumers with more choices and control over their health care decisions.”

Senate health committee Chairman Lamar Alexander, R-Tennessee, added: “Republicans are ready to reduce the cost of health care so more people can afford it, put patients back in charge, and restore freedom and choice to the health care market.”

But GOP members of Congress have not advanced a single alternative to the Affordable Care Act in more than five years, despite repeated pledges to offer a replacement.

And several of the blueprints that senior Republican lawmakers have offered incorporate many of the law’s key protections into their own proposals, including guaranteeing coverage and providing government assistance to help consumers purchase insurance.

Today, some 10 million Americans, many of them previously uninsured, get health coverage through marketplaces created by the law.

Another 11 million low-income people have signed up for Medicaid, mostly in states that expanded their programs with federal funding made available through the law.

That has fueled a historic coverage expansion. In the first quarter of this year, 11.9 percent of adults in the U.S. lacked insurance, down from 18 percent in the third quarter of 2013, before the current expansion began, according to Gallup.

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