On the eve of Tuesday's Tennessee primary, Colorado Sen. Gary Hart's state campaign coordinator, Will Cheek, observed that, "There's a whole lot of people who don't want [Walter F.] Mondale but don't know Gary Hart. They tried one experiment with Jimmy Carter and feel like they got burned, so they're going to play it safe--or just stay home."

As it turned out, many did stay home. The low turnout crushed Hart's hopes for "a second New Hampshire" upset of Mondale.

One reason the Tennesseans felt they did not know Hart was that no one in their congressional delegation said a word on his behalf. Tennessee has one Democratic senator and four Democratic representatives who--like Hart--are under 50 and have served less than 10 years on Capitol Hill. Not one supported him.

That silence was politically costly to Hart, 47, and, unfortunately for him, all too typical. It is one of the major reasons Hart was unable to exploit his early breakthrough against Mondale and why he is struggling to deny Mondale the nomination.

Last week, Oliver (Pudge) Henkel, Hart's national campaign chairman, again described his candidate to a group of reporters as "the representative of a new generation" in American politics. But if Hart does represent that generation, he has won a singularly small mandate from that generation's other officeholders.

The failure is particularly striking, since many of Hart's contemporaries and juniors in Congress and state capitols share his skepticism about foreign-policy formulas and domestic nostrums that once were standard Democratic doctrine. Many of them have pursued the elusive "new ideas" that Hart sought to make his campaign theme.

But few have supported Hart.

That failure has hurt Hart by denying him credible supporters who might vouch for his credentials to their constituents, many of whom are unfamiliar with Hart's record and views.

The Tennessee situation was not unusual. Other than Hart's home state of Colorado, the seven states and the District of Columbia choosing delegates between last Tuesday and next Tuesday have 33 Democratic representatives, senators and governors from the "new generation." Under 50 and with less than 10 years in office, they share many of Hart's experiences and views.

Only two, Reps. Martin Frost (D-Tex.) and Frank McCloskey (D-Ind.), have endorsed Hart. A third, Rep. W.J. (Billy) Tauzin (D-La.), has expressed a "preference" for him. Jesse L. Jackson, the third candidate for the Democratic nomination for president, has one supporter in the group. Mondale, the supposed "old guard" representative, has the backing of 10.

Among "new generation" senators who presumably know Hart well, only Sen. Christopher J. Dodd (D-Conn.) has endorsed Hart. Mondale has the support of four; three had endorsed Sen. John Glenn (D-Ohio) before he withdrew; seven others, including the six who are running for reelection this year, are taking no position.

When Hart was asked in an April 9 interview with The Washington Post about this lack of support from colleagues of his generation, he responded that "very few elected officials really feel a responsibility to move the party forward. Most of them, even if they are frustrated with the status quo, are waiting for somebody to come in at the top and liberate their energies."

Hart also said that "most politicians tend to be cautious. They would rather be safe than right most of the time."

While Hart emphasized qualities of his colleagues that may have braked any impulse to support him, others--speaking anonymously--said Hart's personality was as much of a barrier.

"He's not that well-liked," said a veteran Senate aide. "He's pretty much a loner."

A senator who backed one of the dropout Democratic contenders and was courted heavily by Hart supporters in March said, "I have a great deal of respect intellectually for Gary, but I'm not sure at all about his temperament in the presidency . . . . "

One of Hart's congressional supporters said that some who have spurned Hart have presidential ambitions and thought, before New Hampshire, that "1988, not 1984, would be the year for our generation to make its move."

"Don't forget," he said, "this is a place with pretty big egos. Bob Squier the Democratic media consultant told Gary after New Hampshire, 'Don't let the applause fool you. A lot of it is the sound of hands hitting foreheads.' "

In the early, long-shot days of his candidacy, Hart--perhaps in recognition of his reputation as "a loner"--tried to build bridges to Democratic backbenchers in the House by asking fellow Colorado Democrats, Reps. Patricia Schroeder, Timothy E. Wirth and Ray Kogovsek, to organize get-acqauinted coffees with their friends. The turnouts, Schroeder recalls, were small and the response "good" but muted.

When Hart appeared before the House Democratic Caucus last fall, in its series of interviews with presidential contenders, a couple dozen members showed up, a leadership aide said. But "after New Hampshire," Schroeder said, "everybody wanted to know about Gary." And he once spent an hour in the House cloakroom visiting with members.

But only five House members--three Californians and two New Yorkers--endorsed Hart after his New Hampshire win. And in the Senate, only Dodd and former contender Ernest F. Hollings (D-S.C.) boarded the Hart bandwagon.

Schroeder offers three explanations of this skimpy harvest: "A lot of members did what politicians always do when they're surprised; they pulled back in caution and tried to figure out what to do."

Second, she said, "We were hurt--on this as on other things--by the fact that we haven't had a 'good bench' in the Hart campaign. We're such a small campaign and such a small delegation, we really didn't have as many contacts as we should have had."

Third, she said, "The Mondale people really called in their chits after New Hampshire, and his labor backers were really beating up on the congressmen they support to keep them from bolting. To go for Hart was like throwing yourself under a train."

Richard Moe, a Washington attorney and former Mondale chief of staff, who has directed Mondale's liaison efforts on Capitol Hill, said that Schroeder exaggerates labor's role--and misses the main point.

"Labor was helpful in some cases," Moe said, "but most of the members support Mondale because of who he is and the time he has spent with them on the Hill and in their districts. They are very comfortable with him. Hart has never spent much time on the House side, but even in the Senate, lots of them don't feel they know him well."

Undoubtedly, Mondale's dominance over Hart among elected officials of Hart's "generation" is the result of all these factors.

The latest significant battle was for the endorsement of Ohio Gov. Richard F. Celeste, 46, who became available after his home-state favorite son, Glenn, withdrew.

Celeste is a close Cleveland friend of Hart's manager, Henkel, and has spoken in interviews for the past five years of a coming generational shift in national leadership--using words that anticipated Hart's rhetoric. But after meeting with all three contenders, Celeste endorsed Mondale.

Cynics said labor "delivered" the governor. But Celeste, in an interview, said that Mondale "campaigned with me" in 1978 when he lost his first bid for governor.

"He swore me in as Peace Corps director the next year. And when we won our tax referendum last November, even though he knew I was supporting John Glenn, Fritz Mondale was the first person outside the state to call with congratulations."

But Celeste said he still thinks that generational change is on the way. "The process is just beginning," he said. "A lot of us in Gary's generation are just getting our feet on the ground politically. He's probably a couple laps ahead because of his determination . . . but I'm not sure one candidate is enough to take a whole generation into power. After all, we're very competitive."