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The bottom line, opponents say, is that until Mr. Obama’s health care overhaul was enacted, the government never required Americans to purchase a commercial product from a third party — and the court would be venturing into new territory if it gave the Obama administration the go-ahead.

“As a general rule, you have a much harder row to hoe if you’re trying to get the court to do something new,” said Robert Alt, a senior legal fellow at the Heritage Foundation.

Financial strings

On the Medicaid challenge, the states also have argued that the government is trying to do something it hasn’t done before — in degree if not in kind.

They say the expansion demanded is so massive — requiring states to cover residents making up to 133 percent of the federal poverty level in their programs — and involves so much federal money that even though individual states can technically opt out of the program altogether and turn down Washington’s money, it would be politically suicidal to do so.

“There are multiple states that receive more than $1 billion in funding,” Mr. Alt said. “You can’t just opt out.”

The administration and supporters said that allowing states to reject the Medicaid rules could permanently alter their relationship with the federal government and would threaten to dismantle federal-state programs in areas such as education, child welfare, highway safety and discrimination.

When Congress, for instance, decided to raise the national drinking age to 21, it told states with lower drinking ages that they would get fewer federal highway dollars unless and until they “voluntarily” changed their laws.

“This would upset the nature of our federal government far more than if they decided the mandate is unconstitutional,” Mr. Jost said. “There goes dozens and dozens and dozens of federal programs, and it would have a radical effect on the nature of federalism in the U.S.”

Each side is punctuating its arguments with charges that the other side can’t find a limiting principle.

Randy E. Barnett, a Georgetown law professor who is helping the National Federation of Independent Business, pointed to a 1987 case in which the Supreme Court said the federal government can attach strings to federal dollars — but acknowledged that there is a point at which the financial inducements can become coercive.

“Whereas the government has offered no limiting principle whatsoever to its claim of power under the commerce clause, the Supreme Court itself in South Dakota v. Dole offered the distinction between incentives and coercion,” Mr. Barnett said.

Ian Millhiser, a policy analyst for the Center for American Progress, said it’s “just silly” to call the Medicaid expansion coercive. That has never been a reason for the Supreme Court to strike down a federal spending program, he said.

On the individual mandate, he said, it’s a “red herring” for opponents to suggest that it would destroy limits on federal authority.

“There are many, many laws that cannot be enacted under Congress‘ ability to regulate commerce,” he said. “Non-economic laws such as a federal murder law, a federal rape law, a federal assault law, a federal child-neglect statute, a federal anti-truancy law or a federal law regulating sexual morality all exceed Congress‘ authority under its enumerated constitutional powers.”