WASHINGTON – The chief justice of the United States, William Rehnquist, is being treated for thyroid cancer, the Supreme Court disclosed yesterday, triggering speculation over the judge’s health a week ahead of a presidential election that promises to be even more litigious than in 2000.

Dozens of election-related legal challenges have been launched in lower courts across the country, and several have the potential to reach the top court, specialists in election law said.

The fragile health of the judge, who is 80,also reminded voters and political activists that the next president will have the power to affect the ideological balance of the court, which often divides five to four on controversial issues. The membership of the high court has not changed in a decade.

The chief justice underwent a tracheotomy Saturday at Bethesda Naval Hospital and is expected to be back on the bench when the court reconvenes Monday, court officials said. They offered no further information on his condition or treatment.

A specialist in thyroid cancer at the National Cancer Institute said there are a half-dozen variants of the disease, some of which can be treated more easily than others. Treatment can include removing the thyroid gland or giving the patient injections of radioactive iodine.

“The outcome is very different and treatment is very different depending on what kind of cancer it is, how extensive it is now, how he is treated, and how he tolerates the treatment,” the specialist, Paul Wallner, said. He is chief of the clinical radiation oncology branch in the division of cancer treatment and diagnosis at the institute.

A tracheotomy, the insertion of a tube into the throat to facilitate breathing, is often done as routine preparation for further surgery but may be done to ease breathing in a patient with swelling in his throat that could be due to advanced disease.

While several members of the court have survived cancer, the news left open the possibility that the chief justice could be unable to hear a crucial election case. In that case, the remaining eight judges could rule on their own. In the case of a four-to-four tie, the lower court’s opinion would be affirmed.

Appointed to the court by President Nixon in 1972 and elevated to the chief’s position by President Reagan in 1986, the Milwaukee native has been a reliable conservative vote.

The news of his illness hit conservative activists like a “bolt of electricity,” said the executive director of the Committee for Justice, Sean Rushton. His group advocates the appointment of conservative judges.

Mr. Rushton, while unwilling to entertain the idea of Mr. Rehnquist’s being too ill to continue judicial duties, said the prospect of his departure would galvanize conservative voters who perceive the court not as dominated five to four by conservatives, but as delicately balanced with three committed conservative judges, three committed liberals, and two swing-voters who often break ties, Justices O’Connor and Kennedy.

“Our position is quite tenuous potentially, and just holding ground may be a struggle,” Mr. Rushton said. “To replace Rehnquist with somebody equal to him is an uphill battle. It requires the right president to be elected, the nomination of a person of high caliber, and that person making it through an increasingly difficult and partisan confirmation process.”

He speculated that news could sway to President Bush some moderate voters who oppose judicial rulings in favor of gay marriage, for example.

But the prospect of court appointments is also galvanizing liberal voters, and supporters of abortion rights, according to the president of the Alliance for Justice, Nan Aron. Her group promotes liberal judicial appointments.

“It’s an important reminder of how this election will affect the future of the federal courts, and reminds us that this is one of the few choices a president makes that affects our lives not just for four years, but for 40,” she said.

Mr. Bush mentioned appointments yesterday during a campaign appearance in Greeley, Colo.

“I’ll name judges who know the difference between personal opinion and the strict interpretation of the law,” he said.

Mr. Kerry has said he would not appoint a judge who would “undo a constitutional right,” including a woman’s right to have an abortion.

The court’s party-line ruling in the case of Bush v. Gore has led to speculation that the judges are influenced by their political preferences.

In comments over the weekend, a Clinton appointee who took part in the case, Justice Breyer, said he was unsure whether his judgment had been free of political considerations.

“I had to ask myself would I vote the same way if the names were reversed,” the judge said Saturday at Stanford University Law School, which happens to be the chief justice’s alma mater. “I said ‘yes.’ But I’ll never know for sure, because people are great self-kidders, if I reached the truthful answer.”

Already there have been more lawsuits filed leading up to next week’s election than were filed after the razor thin race in 2000, including several already in Florida, a law professor at the University of Florida College of Law, Clifford Jones, said.

Some suits could eventually be appealed to the Supreme Court. They include a disagreement among federal courts in several states over whether provisional ballots cast at the incorrect precinct should be counted, he said.

The court could be asked to interpret the Help America Vote Act of 2002, which set out minimum standards for state and local governments that administer election, said an election-law specialist at the Moritz College of Law at Ohio State University, Edward Foley. There could also be another Bush v. Gore-style battle over the equal treatment across counties “of provisional ballots instead of hanging chads,” Mr. Foley said.

“There are still quite a few scenarios by which the Supreme Court could be called upon to make a decision that could affect the outcome of the election,” said an election-law specialist at Loyola Law School, Rick Hasen. But for a case to be as decisive as was Bush v. Gore, he said, “You have to have an issue that could determine the outcome of a split state in a situation that could affect the balance of the election.”

Already, the Supreme Court has declined to hear an appeal by an independent candidate, Ralph Nader, of a lower-court ruling that kept him off the Pennsylvania ballot. The high court has not yet decided whether it will hear a similar appeal involving the Ohio ballot.