ASHINGTON, Oct. 25 - The Supreme Court announced on Monday that William H. Rehnquist, the 80-year-old chief justice, had been hospitalized since Friday for treatment of thyroid cancer and that he had undergone a tracheotomy "in connection with" the cancer diagnosis.

While the court said Chief Justice Rehnquist would leave Bethesda Naval Hospital this week and would be on the bench next Monday in time for the next round of arguments, the election-eve announcement was a reminder of the connection between judicial mortality and presidential politics.

While neither presidential candidate has placed great emphasis on the Supreme Court, the chief justice's illness increases attention on the prospect that the next president will have Supreme Court vacancies to fill. It was not clear, however, if either candidate would benefit from heightened public focus on the court.

Thyroid cancer in general is readily treatable, with a cure rate of up to 90 percent. But a small minority of patients have a distinct type of thyroid cancer, anaplastic, that is aggressive and often rapidly fatal. The court provided no information on Chief Justice Rehnquist's type of cancer or on his treatment for it.

Thyroid cancer is treated by surgery or, less often, radiation. The court declined to say whether Chief Justice Rehnquist had had surgery in addition to the tracheotomy, which involves placing a tube through a hole in the throat to prevent or alleviate breathing problems.

Several thyroid cancer specialists not connected with Chief Justice Rehnquist's case said the tracheotomy suggested that the cancer had advanced to the point of pressing on the trachea and interfering with breathing.

"It implies some obstruction and suggests local invasion," Dr. Leonard Wartofsky, a thyroid cancer specialist at Washington Hospital Center here, said in an interview. That would be "not good" for the chief justice's long-term outlook, Dr. Wartofsky said.

In the weeks since the court returned from its summer recess, Chief Justice Rehnquist's voice has been notably husky, as if he were suffering from a cold. Dr. Wartofsky said the huskiness might be explained by the fact that the nerves controlling the vocal cords pass under the thyroid gland. A tumor pressing on a nerve can create hoarseness, he said.

Chief Justice Rehnquist has been a lifelong smoker, but smoking is not a risk factor for thyroid cancer, according to the American Cancer Society. About 23,600 people are given diagnoses of thyroid cancer each year in the United States - about three times as many women as men - and 1,500 people die from it. The seriousness of the disease tends to rise with age.

The news of the chief justice's illness, announced in late morning, created an immediate stir in political circles. Republicans tended to play down the potential impact, while Democrats saw it as an opportunity to try to win over ''persuadable'' voters who had not yet committed to a candidate.

"Anybody who is sophisticated enough to worry about the makeup of the Supreme Court has already decided whom they're going to vote for," said Neil Newhouse, a Republican pollster. "So it may be important, but it's important to people who've already decided how they're going to vote."

Similarly, Connie Mackay, a lobbyist for the Family Research Council, which promotes conservative views on social issues, said, "I don't think it changes anything because the court has not been as out front as an issue as it has been in past elections." But Ms. Mackay said her organization would send e-mail messages "reminding our constituents that once again, we've got to think clearly and get out to the voting polls so that the right person is elected to make the right appointments."

Liberal groups said they hoped to use the Rehnquist news to prod uncommitted voters to choose Senator John Kerry.

Elizabeth A. Cavendish, interim president of Naral Pro-Choice America, which supports abortion rights, said that "the fragility of the court has always been an issue." But, Ms. Cavendish said, the Rehnquist news "crystallizes the point that many of the justices are older or have health problems and the next president will either protect or overturn a woman's right to choose."

She said that her group's final campaign literature was already in the mail but that it would probably send last-minute e-mail messages to voters whom it has identified as favoring abortion rights but either "soft" in their support for Mr. Kerry or planning to vote for President Bush.

"The way to make a difference in an election is to reach new people who have some sort of gap in their thinking," Ms Cavendish said.

Ralph G. Neas, president of People for the American Way, a liberal group, said, "There is no question that the timing of this allows us to raise this issue and put it in play." He noted that a recent Time magazine poll had found that 86 percent of people surveyed said that appointments to the Supreme Court over the next four years were either very important (59 percent) or somewhat important (27 percent) in their voting decision.

When asked in the poll, on Oct. 15, whether the issue would make them more likely to vote for Mr. Bush or Mr. Kerry, 38 percent said it would make them more like to vote for the president and 43 percent said it would make them more likely to vote for his Democratic challenger.

Chief Justice Rehnquist, who turned 80 on Oct. 1, is the second-oldest person ever to serve as chief justice. The oldest was Roger Brooke Taney, who died in office in 1864 at the age of 87. Except for orthopedic problems, Chief Justice Rehnquist has generally been in good health. He had back surgery for a herniated disc in 1995 and knee surgery in 2002 to repair a tendon he injured in a fall.