The Supreme Court began its new term Monday with a complicated case about whether those who provide care and receive benefits under the Medicaid program for the poor can go to court when a state tries to cut spending on the program.

California, which for budget reasons reduced its reimbursement rate for the program by 10 percent, and the Obama administration say individuals do not have a right to go to court. They say only the federal government may determine whether the rates paid to doctors and other providers are proper under the federal Medicaid law.

But Washington lawyer Carter Phillips, representing the private plaintiffs, said they must have some access to the courts when a conflict arises.

“My people have a life-and­-death problem,” Phillips told the court.

It was the first case of a term that could be the most momentous since John G. Roberts Jr. became chief justice six years ago. It is likely that the court will determine the constitutionality of the 2010 health-care act before adjourning in June, as well as take on a weighty docket that raises other questions about the limits of federal power.

The court did not take additional cases Monday, but it did dispose of nearly 2,000 petitions that had accumulated during its summer recess.

Among the cases the justices decided not to hear was a challenge from a Maryland gun owner who said the state’s process for granting permits to carry handguns outside the home was so restrictive that it violated the Second Amendment. The justices made no comment, but Maryland had argued that other cases were better suited if the court was interested in addressing the question of gun possession outside the home.

The court began its day by recognizing Justice Antonin Scalia’s 25th anniversary on the court, with Roberts noting that Scalia first heard oral arguments on the first Monday in October 1986.

“The place has not been the same since,” Roberts said to laughter from colleagues and others in the courtroom.

At the end of an hour of oral arguments in the Medicaid case, it was not apparent that a majority view had emerged.

Medicaid is a cooperative program between the states and the federal government to provide health services to the poor and those with disabilities. In return for federal money, states must ensure that their payments are “sufficient to enlist enough providers to that care and services are available.”

A federal agency makes that determination, and it eventually ruled that California’s cuts in 2008 and 2009 violated the standard. That process is under appeal.

In the meantime, Medicaid providers, beneficiaries and others hurt by the cuts went to state and federal courts and won injunctions against the state’s new rates.

California Deputy Attorney General Karin S. Schwartz told the court that the federal Medicaid law does not provide any opening for private plaintiffs to go to court to challenge state reimbursement decisions.

“If Congress wants to provide for private-party litigation, it must do so clearly and unambiguously, and it has not done so in this case,” Schwartz said.

But Justice Elena Kagan said California attempted an “end run” around the process by putting its new rate schedules into effect before seeking approval from the federal government.

Justice Ruth Bader Ginsburg noted that only the private plaintiffs could go to court to get an injunction against the new rates. “The government can’t stop that from happening, even if the government thinks that they are in violation of the Medicaid Act,” Ginsburg said.

Schwartz replied that the government could cut off funding to California.

“Yes, but that’s a very drastic remedy that’s going to hurt the people that Medicaid was meant to benefit,” Ginsburg said.

Roberts seemed to agree with Schwartz that Congress had not provided for private litigation, and others worried about judges getting involved in what is a complicated rate-setting process best handled by professionals.

Phillips said those who lack access to “vital medical care” need the option to go to court. And he said the injunction only attempted to keep the rates from going into effect until the federal agency decided whether they were proper.

The case is Douglas v. Independent Living Centers of Southern California .