Not a single justice of the Supreme Court is resigning. Contrary to the hopes of some, hopes that became rumors and even news stories, everyone is staying, some defiantly.

"It's a bald-faced lie," Justice Thurgood Marshall growled over the telephone when asked again whether he even considered resigning to allow Jimmy Carter a liberal appointment. That had been the hope of some liberals, thinking that Carter could sneak in a liberal replacement for Marshall, 72, or Justice William J. Brennan Jr., 74, before Ronald Reagan could put in a conservative. Now the hope of liberals is that Brennan and Marshall can outlive the Reagan administration, for neither man budged.

"I'm serving out my term," Marshall said. "And it's a life term."

Brennan is staying as well, despite a period a year ago when friends say he contemplated resigning because of poor health. Acquaintances say that Brennan is feeling better now.

So here is the only branch of government where nothing is changing. There are no moving vans here, no one making last-minute decisions to preempt his successors and no one scurrying around looking for a job. Jimmy Carter leaves offices as a president unable to make a single Supreme Court appointment. The other time that happened was during the administration of Andrew Johnson, who left office in 1868.

As Carter departs, so do the dreams of the Griffin Bells and the Shirley Hufstedlers, to name just two, who might have been his nominees to the Supreme Court. A new crop of guesses takes their place: Carla Hills, the former housing and urban development secretary, as the first woman justice; William Coleman, the former transportation secretary and the first black Supreme Court law clerk, as a replacement for Marshall or as the second black justice; Robert Bork, former solicitor general and a Yale Law professor, known for his conservative views on antitrust and government regulation; Prof. Philip Kurland of the University of Chicago, who became well-known in this area for helping the city of Richmond fight off school busing, and even anti-Equal Rights Amendment activist Phyllis Schlafly, the only one of the above to mention her own name prominently since Nov. 4.

"I certainly think I should be considered," she said.

Reagan may get anywhere from zero to five appointments during four years in office. Five of the current justices (Chief Justice of the United States Warren E. Burger, 73; Lewis F. Powell Jr., 73; Harry A. Blackmun, 72; Marshall, and Brennan) are aging and some have had health problems.

The fact that this has become, again, a court of old men is constantly underscored by the behavior of the press, always considered tasteless by court officials. There is, for example, a monthly rumor that a certain justice is dead. It produces frantic calls to the court's public information officer for confirmation or denial.

Each time a justice fails to appear on the bench for oral arguments or an opinion, there are demands to know why. Is he ill? Is he close to death? Will he resign?

Liberals had hoped someone might leave before Carter left office. The votes on major controversies -- like affirmative action and government regulation -- are 5 to 4 or plurality votes. The replacement of one pro by one con, or vice versa, could swing a lot of issues.

Most lawyers caution that even if Reagan gets several appointments, it is extremely difficult for a president to infuse the court with his own ideology. It is hard, they say, to find a respectable candidate who is wholly idealogically pure. And even if one is found, these people are notoriously independent. They no longer need the president who appointed them once they are on the bench.

For, as Marchall pointed out, "it's a life term."