Washington ? Concluding three days of fervent, public disagreement, a Supreme Court seemingly split over ideology will now wrestle in private about whether to strike down key parts or even all of President Barack Obama’s historic health care law. The justices’ decision, due this June, will affect the way virtually every American receives and pays for care.

The court wrapped up public arguments Wednesday on the overhaul, which is designed 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 argument time was unusual in that it assumed 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 houses. The justices’ decision is sure to become a significant part of this year’s presidential and congressional election campaigns, in which Republicans have relentlessly attacked the law.

Both liberal and conservative justices appeared on Wednesday 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 cover people regardless of their 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 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 the 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.

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, retorted 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.”