WASHINGTON — The survival of President Barack Obama’s health care overhaul rests with a Supreme Court seemingly split over ideology and, more particularly, in the hands of two Republican-appointed justices.

Chief Justice John Roberts and Justice Anthony Kennedy put tough questions to administration lawyers defending the health care law during three days of arguments that suggested they have strong reservations about the individual insurance requirement at the heart of the overhaul and, indeed, whether the rest of the massive law can survive if that linchpin fails.

But Roberts and Kennedy also asked enough pointed questions of the law’s challengers to give the overhaul’s supporters some hope. In any event, justices’ questions at arguments do not always foretell their positions.

The court’s decision, due in June, will affect the way virtually every American receives and pays for health care and surely will reverberate in this year’s campaigns for president and Congress. The political effects could be even larger if the court votes 5-4 with all its Republican-appointed justices prevailing over all the Democratic appointees to strike down the entire law, or several important parts of it.

Not since 2000, when the court resolved the Bush v. Gore dispute over Florida election returns that sealed George W. Bush’s election as president, has a Supreme Court case drawn so much attention.

The court wrapped up public arguments Wednesday on the overhaul, which aims to extend health insurance to most of the 50 million Americans now without it. The first and biggest issue the justices must decide is whether the centerpiece of the law, the requirement that nearly all Americans carry insurance or pay a penalty, is constitutional.

Wednesday’s morning session was unusual in that it assumed, for purposes of argument, a negative answer to that central question. What should happen to other provisions, the justices and lawyers debated, if the court strikes down the requirement? If the justices are following their normal practice, they had not even met to take a preliminary vote in the case before all argument concluded.

Questions at the court this week showed a strong ideological division between the liberal justices who seem inclined to uphold the law in its entirety and the conservative justices whose skepticism about Congress’ power to force people to buy insurance suggests deep trouble for the insurance requirement, and possibly the entire law.

The divide on the court reflects a similar split in public opinion about the law, which Congress approved two years ago when Democrats controlled both the House and Senate.

Liberal and conservative justices alike appeared to accept the administration’s argument that at least two important insurance changes are so closely tied to the must-have-coverage requirement that they could not survive without it: provisions requiring insurers to extend coverage to people with existing medical problems and limiting how much those companies can charge in premiums based on a person’s age or health.

Less clear was whether the court would conclude that the entire law, with its hundreds of unrelated provisions, would have to be cast aside.

The justices also spent part of the day considering a challenge by 26 states to expansion of the federal-state Medicaid program for low-income Americans — an important feature which alone was expected to extend coverage to 15 million people and which no lower court has rejected. The conservative justices appeared open to the states’ argument that the expansion is unconstitutionally coercive.

Audio of Wednesday morning’s argument can be found at: http://apne.ws/GX1p23 ; the afternoon argument at: http://apne.ws/GXdZOP .

Solicitor General Donald Verrilli Jr. took a few seconds at the end of the Medicaid argument to make a final plea for the court to uphold the entire law, which he said would “secure the blessings of liberty” for millions of Americans by providing them with affordable health care.

Verrilli told the court that Congress had made a policy decision to fight the high cost of medical care through the new law. “I would urge the court to respect that judgment,” he said.

Paul Clement, the lawyer for the states challenging the law, answered that it would be a strange definition of liberty to make people who may not want it buy health care insurance. And he called Congress’ threat to cut all Medicaid funding from states that refuse to expand the program “a direct threat to our federalism.”