EVEN before President-elect George Bush takes the oath of office next January, the campaign to succeed Gov. Michael S. Dukakis as Bush's Democratic challenger will have begun in earnest. In the upcoming four-year campaign for the 1992 nomination, the Democrats can look forward to more internecine squabbling and ideological blood-letting. Scarcely a week after the election, the battle lines are already drawn for 1992.

In 1988, the Republicans ran a candidate who, by many accounts, should not have won. Despite the surface appeal of "peace and prosperity," the public's distaste for Bush and widespread uncertainty about the nation's economic future dealt Republicans their worst opening hand since the post-Watergate campaign in 1976. Yet the Democrats still could not trump it.

For 1992, the Democrats desperately need to find a candidate who can appeal to a coalition broad enough to win. After losing five of the last six presidential elections--four by landslides--the Democrats are grasping for another approach.

THE party's left wing blames the loss on Dukakis for trying to run from his ideological roots. They insist that, had Dukakis made a cogent defense of liberalism and inspired voters, rather than allowing Bush to distort the word "liberal" into a verbal cudgel roughly equivalent to "child molester," he could have beaten Bush. "Next time," they say, "we shouldn't hide our liberal colors."

Democratic moderates counter that the voters have resoundingly rejected "traditional" liberalism and that the party must nominate a candidate acceptable to Southern conservatives if they ever hope to break the Republican lock on the electoral college.

In a sense, both groups long for the same unattainable goal--resurrecting some variant of the New Deal coalition. The left wing deludes itself to think that the Democrats can nominate a traditional liberal and still appeal to "middle America." The last three elections show that they can't. Similarly, the moderates hope to nominate a Republican clone and still retain the loyalty of minorities and liberals--which is equally impossible.

Both sides are already touting their contenders. The left will unite behind Jesse Jackson, who should be the de facto front-runner for the next three years. But Jackson will not win the nomination. Although most Jackson supporters are ardent, the marginal supporters--myself included--who chose him only because of the mediocrity of the 1988 field will jump ship if offered a more attractive candidate.

The conservatives and moderates hope for Sen. Sam Nunn (D--Ga.) or former Virginia Governor and Senatorelect Charles Robb. But it's not going to happen. In addition to serious ideological liabilities (Nunn has been weak on civil rights and strong on nerve gas and SDI), each of the two faces personal obstacles. Compared to Nunn, even Dukakis bubbles with charisma, and there are rumors that Robb's social life makes Gary Hart's look monastic. (Even unsubstantiated rumors are politically damaging, as Dukakis knows all too well.)

ONE solution to the Democrats' dilemma is, oddly enough, an intellectual, technocratic, dull. Northeastern liberal who doesn't trumpet his liberalism.

No, not Mike Dukakis again. The man who can win for the Democrats is Bill Bradley. The popular New Jersey Senator is a Rhodes scholar, former professional basketball player, and a highly respected man on Capitol Hill. He has been an architect of progressive policies such as tax reform.

In addition, he has the one quality needed to win that Democrats too often lack--a reputation for a solid understanding of defense issues. While hardly a hawk. Bradley avoids the image of knee-jerk anti-militarism that afflicted Dukakis. After twelve years of Republicans in the White House, fielding a candidate whose primary flaw is one vote for Contra aid should not be too bitter a pill to swallow to elect a Democratic President.

Although Bradley cannot hope to match the charisma of, say, Ronald Reagan, he is quite capable of making an ideological appeal to the broad spectrum of "average Americans" that Dukakis courted. (The one exception is Southern conservatives, who will never return to the fold unless the Democrats retreat on civil rights and social issues, which they will never do.)

Bradley is bright without appearing a "pointy-head." He is progressive without appearing "out of the mainstream." He adheres to liberal principles without being burdened by ideological baggage. And he is the Democrats' brightest hope to win the Presidency in 1992.