Washington — If Gary Hart doesn't win the Democratic nomination this year, he could face even tougher competition for the top spot in 1988. Many of his potential foes four years from now would be as young and as enthusiastic about ''new ideas'' as Senator Hart. His theme of a ''new generation'' of leadership could be echoed by most, if not all, of his rivals.
Around the country this year, voters are often heard to say: ''If Senator Hart doesn't win this time, he will be perfectly positioned for the race four years from now.'' But a number of political analysts say that is far from certain.
Analysts say the list of potential candidates for 1988 is already getting long. Among those mentioned: Sen. Dale Bumpers of Arkansas, Sen. Bill Bradley of New Jersey, Sen. Joseph R. Biden of Delaware, Sen. Sam Nunn of Georgia, Sen. Christopher J. Dodd of Connecticut, Gov. John D. (Jay) Rockefeller IV of West Virginia, and Gov. Bruce Babbitt of Arizona.
But the man at the top of just about everyone's list is Gov. Mario M. Cuomo of New York. His speeches are described as ''barn burners.'' His political instincts are rated as near-perfect. And his political appeal extends right across the ethnic and racial lines where a Democratic candidate must do well to win the White House. Says political scientist Norman Ornstein of the American Enterprise Institute: ''Governor Cuomo makes a case that will get the average ethnic Democrat who voted for Reagan in 1980 to think twice.''
Mr. Cuomo, Dr. Ornstein says, ''is the class of the party right now.''
All this would challenge Mr. Hart to find some way to keep his name before the public if he loses the current race to Walter Mondale.
One obvious possibility: to accept the vice-presidential spot on the Democratic ticket, if it is offered. Even if the Democrats lost to President Reagan in the fall, Hart would have an opportunity to make his name and his positions better known.
One of Hart's greatest weaknesses this year has been voters' lack of familiarity with his positions. In New York State exit polls last week, for example, that was the reason most often given by voters for opposing him.
Furthermore, if a Mondale-Hart ticket won this year, Hart, like Vice-President George Bush in the Reagan White House, would be considered the natural front-runner after Mr. Mondale left office.
There's another side of that argument, of course. Would Hart gain the image of a loser if he were on a ticket that was clobbered by Mr. Reagan? Running for vice-president is no guarantee of fame. How many people remember the late William E. Miller of New York? (He shared the ticket with Barry Goldwater in 1964.)
Hints about '88 are already beginning to float around this city. Senator Bumpers said the other day that he's a little bit sorry that he did not try to go all the way this year. He got into the race early, but then pulled out when it looked as if he couldn't raise enough money. Hindsight, especially in light of what Hart managed to do with very little cash, indicates that he should have kept on going, Senator Bumpers said.
Meanwhile, some of the others are known to be privately and quietly making inquiries about what the response might be if they joined the fray next time. Once again, Hart's strong showing, even with little spending in Iowa and New Hampshire for advertising or staff, is encouraging to everyone.
All this talk about new names should not leave out some old names that might also be back in 1988.
The Rev. Jesse Jackson comes immediately to mind. His showing this time, although based primarily on black votes, has been strong enough to encourage speculation that he could be an important factor in Democratic politics for years to come. He could have some competition in 1988 from other black politicians. Mayor Tom Bradley of Los Angeles and Mayor Andrew Young of Atlanta are just two of the possibilities.
Sen. John Glenn, a disappointing performer this year, nevertheless has not ruled out another run.