WASHINGTON —

The way to frame a Supreme Court argument meant to sway Justice Anthony Kennedy is to talk about liberty. It is his touchstone and guiding principle, and his conception of liberty is likely to determine the future of President Obama's health-care law.

If the administration is to prevail in the health-care-law case, it must capture at least one vote beyond those of the court's four more liberal justices, who are thought virtually certain to vote to uphold the law. The administration's best hope is Kennedy.

The point was not lost on Solicitor General Donald Verrilli Jr., who concluded his defense of the law at the court this week with remarks aimed at Kennedy. Verrilli said there was "a profound connection" between health care and liberty.

"There will be millions of people with chronic conditions like diabetes and heart disease," he said, "and as a result of the health care that they will get, they will be unshackled from the disabilities that those diseases put on them and have the opportunity to enjoy the blessings of liberty."

Paul Clement, representing 26 states, including Washington, challenging the law, had a comeback.

"I would respectfully suggest," he said, "that it's a very funny conception of liberty that forces somebody to purchase an insurance policy whether they want it or not."

Kennedy's understanding of liberty is idiosyncratic, and there is every reason to think that both lawyers' arguments in the concluding minutes of the argument Wednesday resonated with him, said Helen Knowles, author of "The Tie Goes to Freedom: Justice Anthony M. Kennedy on Liberty." (The title is telling. Another book on the justice, by Frank Colucci, is called "Justice Kennedy's Jurisprudence: The Full and Necessary Meaning of Liberty.")

"I really don't think Justice Kennedy has any idea at the moment how he's going to vote in these cases," Knowles said.

Counting questions

Indeed, the evidence from the key argument Tuesday, on the constitutionality of the individual mandate — health-care law's requirement that most Americans obtain insurance or pay a penalty — was mixed.

Justices tend to ask more questions of the lawyers whose positions they oppose, and Kennedy posed six questions to Verrilli and just three to the two lawyers challenging the law.

The questions to Verrilli were, moreover, mostly easy to read. They were crisp expressions of discomfort with the administration's arguments.

"Can you create commerce in order to regulate it?" Kennedy asked. "This is a step beyond what our cases have allowed, the affirmative duty to act to go into commerce. If that is so, do you not have a heavy burden of justification?"

"Can you identify for us some limits on the commerce clause?" he asked.

Those questions fit neatly within one strain of Kennedy's understanding of liberty, one he discussed at length last year in an opinion for a unanimous court.

Limiting federal power, he wrote, "protects the liberty of all persons within a state by ensuring that laws enacted in excess of delegated governmental power cannot direct or control their actions.

"By denying any one government complete jurisdiction over all the concerns of public life, federalism protects the liberty of the individual from arbitrary power. When government acts in excess of its lawful powers, that liberty is at stake."

The case concerned a federal prosecution of a domestic dispute. Clement was the lawyer on the winning side.

Responsibility

But there is another strain to Kennedy's conception of liberty, one that may help Verrilli.

"When you think about liberty relative to Kennedy," Knowles said, "the element most important to him will be the idea of individual responsibility. He thinks the government has the power to ensure that the responsible exercise of liberty be done in an educated manner."

That impulse seemed to inform the most closely scrutinized exchange Tuesday.

"The young person who is uninsured," Kennedy told Michael Carvin, a lawyer for private parties challenging the law, "is uniquely proximately very close to affecting the rates of insurance and the costs of providing medical care in a way that is not true in other industries. That's my concern in the case."

Carvin responded that the law actually frustrated individual responsibility.

"They're compelling us to enter into the marketplace," he said, but "they're prohibiting us from buying the only economically sensible product that we would want, catastrophic insurance."

Kennedy's critics say his pronouncements on liberty are empty of real content.

In 1992, joining with Justices Sandra Day O'Connor and David Souter to uphold the core of the constitutional right to abortion identified in Roe v. Wade, Kennedy wrote by way of explanation that "at the heart of liberty is the right to define one's own concept of existence, of meaning, of the universe, and of the mystery of human life." Justice Antonin Scalia later mocked this as the "famed sweet-mystery-of-life passage."

Judge's prose

Writing in The New Republic in 2010, Eric Posner, a law professor at the University of Chicago, said Kennedy's writing could be vapid and disappointing for its lack of rigor.

"Liberty, in his mind, explains the right to abortion, but does not stand in the way of certain limits on abortion," Posner wrote. "In what sense, then, does this commitment to liberty have explanatory power?"

Kennedy may be hard to read, but it does not stop people from trying. The Supreme Court chamber grows a little quieter when he asks a question, and other justices seem to grow more attentive. And the lawyers who argued before him this week indicated intimate familiarity with his writings and a fine-tuned sensitivity to trying to satisfy him.

On hearing that Kennedy had concerns about how young people without insurance affect others' rates, Carvin paused before he answered.

"I may be misunderstanding you, Justice Kennedy," Carvin said. "I hope I'm not."