Whatever their private doubts, Jimmy Carter's delegates from Virginia will arrive in New York this week determined to stand by their man but less than confident that they can persuade their state's voters to do the same this fall.

If Carter wins renomination -- and the state's 59 Carter delegates have no doubt that he will -- Virginia Democratic leaders will be fighting for his reelection as though the party's life depended on it. And in some ways it will. After 12 years of steady Republican election gains, state Democrats can't afford very many more losses. Four years ago, Virginia earned the ignoble distinction of being the only Southern state Carter couldn't carry against Gerald Ford.

There are many Democrats who think the state's largely conservative electorate will be even easier pickings for Ronald Reagan, the GOP nominee, this time around.

"I'm pretty pessimistic about whether Carter can carry Virginia in November," concedes John Melnick, an Arlington lawyer and former state legislator who is a Carter delegate at the Convention. "But as a group, the delegates are gung-ho for the president -- they really like him."

As the economy worsens, the hostage crisis in Iran continues, and Carter's showing in the polls deteriorates most Virginia Democrats cling to the president. Ignoring overtures from supporters of Edward M. Kennedy, who has only five Virginia delegates, they teasingly flash their "Probably Carter Despite Everything" buttons and hope the anti-Carter sentiment will bottom out.

Such loyalty, they explain, is understandable: if you're a Democrat, a realist and a Virginian, Carter is the only logical choice.

"I've always expected Reagan to get the nomination, and Carter is the only candidate who can beat him because he can take the South," says Nancy Arnsen, a Carter delegate from Alexandria. Kennedy, she adds, "could never, ever beat Reagan in Virginia."

Kennedy's Virginia backers dispute Arnsen's reasoning but have been frustrated in their efforts to break the president's hold on the Virginians.

"Delegates should express the current will of the voters, not act like robots," argues Ernest Kessler, Kennedy's campaign coordinator in Virginia. r"It's kind of like getting married. You get engaged and from the engagement to the wedding you can still back out."

Confident Carter will get the nomination, Dottie Schick, who chairs the Fairfax County Democratic Committee, says the Reagan candidacy may be just the thing to turn out Virginia votes. She hopes Democrats and moderate Republicans will consider what a Reagan presidency would be like and conclude, "Oh, my God."

Carter must win Northern Virginia to carry the state. He didn't in 1976 and Schick says the state party will have to work all the harder this year.

"We are all opinion-makers in our communities," she says of active Democrats. "What we think and say makes a difference to people on the fence. dWe have to point out the president's record, what he has accomplished and what he has tried to accomplish."

Some Democrats worry privately that John Anderson's independent candidacy will hurt Carter among Northern Virginia voters who, as one delegate put it, "are not the diehard conservatives that you have elsewhere in the state." This same delegate is also concerned that Carter's trouble with voters may hurt the reelection chances of Northern Virginia's two Democratic congressmen, Reps. Joseph L. Fisher and Herbert E. Harris II.

In New York, however, these nagging worries will be set aside for a while. The Virginia delegates most of whom are attending their first national convention, say they will move into their quarters at the Sheraton City Squire Hotel and lose themselves in the excitement of their party's boisterous get-together.

Despite the failure to deliver for Carter four years ago, the delegates say they are not being penalized or shunted aside in favor of delegations from states where Carter was a winner.

"Virginia is getting a great deal of priority," says John Schell, another delegate from Arlington. The Carter organization, he says, sees Virginia as "a swing state" that could go either way in November.

"We're on the same floor at the hotell as the Georgia delegation, and we're in the front row on the convention floor," Schell boasts. "We're not being ignored by any means."

Something else that is not being ignored in 1981. That's when Virginia's Democrats and Republicans will go head-to-head in statewide elections that already are drawing as much attention as the presidential contest.

"It's definitely on our minds and everybody is jockeying around for positions," says Schick." And we think we have the best candidate a year from now."

The candidate in this case, is Virginia Lt. Gov. Charles S. Robb of McLean. The only Democrat holding statewide office now, he is virtually assured his party's nomination for governor next year. Many Democrats look to him as their best -- and perhaps last -- hope of wresting political control of the governor's office away from Republicans.

Robb's likely GOP opponent is J. Marshall Coleman. Virginia's attorney general. Coleman, regarded skeptically by many conservatives, kept a relatively low profile at the GOP convention in Detroit last month.

But some Democrats expect Robb and party chairman, Richard L. Davis of Portsmouth, who wants to run for lieutenant governor next year, to use the convention as a chance to get some media exposure for the voters back home. t