The high court should strike down the entire law, not just the main requirement that individuals purchase insurance or pay a penalty beginning in 2014, their appeals said.
The filings, on behalf of 26 states and the National Federation of Independent Business, also said the justices should act before the 2012 presidential election because of uncertainty over costs and requirements.
On the issue of timing, their cause got an unexpected boost from retired Supreme Court Justice John Paul Stevens, who said voters would be better off if they knew the law's fate law before casting their ballots next year.
The 91-year-old Stevens said in an Associated Press interview that the justices would not shy away from deciding the case in the middle of a presidential campaign and would be doing the country a service. "It would be better to have that known about than be speculated as a part of the political argument," Stevens said in his Supreme Court office overlooking the Capitol.
The appeals seek to overturn a portion of the ruling by the federal appeals court in Atlanta that struck down the individual insurance requirement.
That court upheld the rest of the law, which the states and the business group say would impose huge new costs.
The law would extend coverage mainly through subsidies to purchase private insurance and an expansion of Medicaid. The states object to the Medicaid expansion and a provision forcing them to cover their employees' health care at a level set by the government.
The filings came on the same day that the Obama administration's response was due at the Supreme Court in a different challenge to the same law. In that case, the federal appeals court in Cincinnati upheld the law.
The individual insurance mandate "indisputably served as the centerpiece of the delicate compromise that produced" the law, according to the states, with Florida taking the lead.
The administration said in the Atlanta-based 11th U.S. Circuit Court of Appeals that reforms in the insurance market, including requiring insurers to cover people without regard for pre-existing health conditions, would not work without the mandate.
The insurance requirement is intended to force healthier people who might otherwise forgo insurance into the pool of insured, helping to reduce private insurers' financial risk.
Both appeals stressed the importance of resolving the overhaul's constitutionality as soon as possible, which under normal court procedures would be by June 2012.
While a decision in that time frame would come in the midst of the presidential campaign, the NFIB said it is more important to resolve uncertainty about costs and requirements than drag out consideration into 2013 or beyond.
"When you talk to our members and other small-business owners about what is the biggest problem they're facing, they say uncertainty," said Karen Harned, executive director of the NFIB's legal division. "When you ask what, one of first answers is the health care law."
Stevens, who retired last year, said his former colleagues would not be affected by the potential impact of their decision on Obama's re-election chances.
"They'll decide it on the law. I'm totally convinced of that," he said.
It is quite likely that the court eventually will rule on the overhaul because it almost always hears cases in which a lower court has struck down a federal law, as the Atlanta-based court did. Less clear is the timing.
Obama appointed Stevens' successor, Justice Elena Kagan. But Stevens said that if he still had a vote on the court, he would cast it in favor of hearing the case sooner rather than later.
He would not say how he would vote on the issue of the law's constitutionality, although he said the court's 6-3 decision in a 2005 case involving medical marijuana seems to lend support to the administration's defense of the law.
Stevens wrote the opinion that held that the Constitution allows federal regulation of homegrown marijuana as interstate commerce. A central dispute in the health care case is over Congress's power under the Constitution's commerce clause to mandate the purchase of health insurance.
In addition to the competing rulings on the law's validity, a federal appeals court in Richmond, Va., ruled that it was premature to decide the law's constitutionality. Citing a federal law aimed at preventing lawsuits from tying up tax collection, that court held that a definitive ruling could come only after taxpayers begin paying the penalty for not purchasing insurance.
The federal appeals court in Washington also heard arguments in yet another lawsuit against the overhaul last week. That court has no timetable for its decision.
The other states aligned with Florida are: Alabama, Alaska, Arizona, Colorado, Georgia, Idaho, Indiana, Iowa, Kansas, Louisiana, Maine, Michigan, Mississippi, Nebraska, Nevada, North Dakota, Ohio, Pennsylvania, South Carolina, South Dakota, Texas, Utah, Washington, Wisconsin and Wyoming.