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They are two of the most compelling figures in American politics and, increasingly, two of the most irrelevant.

New York Gov. Mario Cuomo says he doesn’t want a seat on the Supreme Court, or at least not the one that becomes available later this year when Justice Byron White retires. He wants to stay in Albany, N.Y., Cuomo says, and perhaps seek a fourth term as governor in 1994.

Jesse Jackson, who ran twice for president, withdrew his name from consideration as executive director of the NAACP. Something about a rules change, Jackson said, some bureaucratic wrinkle that might diminish the power of the office.

For more than a decade, legions of Democratic admirers have wondered what Cuomo and Jackson wanted, while legions of detractors wondered what they were up to. And three months into Bill Clinton’s presidency, the answers to those questions are no clearer.

These days, with a Democrat in the White House, Cuomo won’t leave his desk in the governor’s mansion, while Jackson won’t get behind a desk and run something besides his Rainbow Coalition.

For millions of liberals, Cuomo and Jackson are living embodiments of traditional Democratic Party values. Passionate in their beliefs and articulate in carrying them to the public, they lifted the spirits of the party faithful during the long years of exile from the White House.

Now, while Clinton battles with deficit reduction and health-care reform, Cuomo plays middleman between media mogul Rupert Murdoch and the antic staff of the beleaguered New York Post.

Jackson, for his part, keeps lonely vigils outside Major League Baseball parks, drawing no public support from any active ballplayer in his quest to secure more front-office jobs for minorities.

Both men swing in the outer orbits of public life, Jackson flitting from issue to issue, from corporate racism to the politics of Haiti to his TV talk show on CNN to statehood for the District of Columbia, where he serves as an elected “shadow” senator.

While he keeps regular office hours, Cuomo seems to find meaning in an endless round of budget battles with legislators and in the precarious fiscal condition of New York state.

There was a time when it looked as if different political fates might have awaited both men.

While few Americans can recall what Clinton said last week, millions remember Cuomo’s speech to the 1984 Democratic National Convention and Jackson’s convention address four years later in Atlanta.

In 1984, in San Francisco, Cuomo was the keynoter, unburdening himself of a speech that called the Reagan administration to account.

“A shining city is perhaps all the president sees from the portico of the White House or the veranda of his ranch, where everyone seems to be doing well,” Cuomo said, presaging the argument Democrats would make against Ronald Reagan’s successor in 1992.

“The Republicans believe that the wagon will not make it to the frontier unless some of the old, some of the young, some of the weak are left behind by the side of the trail,” Cuomo continuned.

Four years later, Jackson wove a speech that bedazzled his fiercest critics, a speech that parents in some American families would recite to their children.

“Every one of those labels they put on you . . . in the projects, on the corners, I understand,” Jackson said. “Call you outcast, low down, you can’t make it, you’re nothing, you’re from nobody, subclass, underclass-when you see Jesse Jackson, when my name goes in nomination, your name goes in nomination.”

When the nation turned away from George Bush, however, they turned to the governor of Arkansas, a self-proclaimed “new Democrat,” and to a Texas billionaire with an anti-government message.

Jackson chose to sit out the early stages of the last election cycle, toying with endorsements for other Democrats before signing on with Clinton.

In the interim, Clinton, a Southern governor who had reached out to a different generation of black leadership, used Jackson as a foil to appeal to Reagan Democrats.

Cuomo, meanwhile, did a poor job hiding his lack of enthusiasm for Clinton. After declaring his lack of interest in the nomination, he flirted with loyalists who wanted him to get into the race during the New Hampshire primary, during the New York primary and even during the runup to the party convention.

Now, with the political landscape altered, Cuomo and Jackson find themselves laboring to avoid the past tense.