In between bites of shrimp and crab claws at a recent reception in McLean, some people went up to Virginia Gov. Charles S. Robb and asked for his autograph.

"It's something of an affront," Robb said, laughing afterward. The requests are never for something "I've done," Robb explained. They always seem to say: "I'm going to save this because someday you're going to be . . . . " His voice trails off.

Robb, 46, who leaves office Jan. 11 as one of Virginia's most popular governors, said he knows the admirers are drawn by speculation that he may run for national office in 1988. But for the moment he said he would like to be remembered for his four years as governor in Richmond.

Yet it is Robb's accomplishments in the old capital of the Confederacy that has given the son-in-law of President Lyndon B. Johnson many of his national followers.

To them, Robb embodies many of the elements that they say the national Democratic Party desperately needs: A fiscal conservative who had combined support for social programs with a concern for the minorities who have long been crucial to any national Democratic campaign.

That, plus the Democratic sweep in Virginia last fall, make Robb a natural candidate "whether he wants it or not," said Robert Strauss, former chairman of the Democratic National Committee.

"Any politician would be flattered," Robb countered, all the while disavowing any "present plans" to seek public office again. He maintains the extensive attention and news media coverage are a "boomlet" that will fade away after "the word 'former' goes in front of my name."

Robb was first mentioned for national office when he led a Democratic resurgence with his election as Virginia governor in 1981 and then moved to set the tone of a socially committed, but fiscally conservative, administration.

He boosted his standing Nov. 5 when Democrat Gerald L. Baliles, campaigning as Robb's rightful heir, repeated the sweep of statewide offices that included electing the first black and the first woman statewide in Virginia.

While that has some of Robb's followers ready and willing to raise funds for a national race, a number of politicians question whether Robb is presidential material.

"I predict he will become 'the greatly mentioned' of American politics, touted for every office from the presidency of the United States to the ambassadorship to the court of the king of Belgium," said former Virginia legislator Ray L. Garland, a Republican.

Garland has railed against Robb in a Roanoke newspaper column he writes, calling him an "overachiever" who was both benefited and bedeviled by his White House marriage to Lynda Bird Johnson. He said Robb was a man who had set "a great, difficult goal in a calling that did not come naturally to him . . . and may surprise some people by leaving elective politics alone."

Rep. Mickey Leland (D-Tex.), chairman of the DNC's black caucus and a friend of Robb's wife, said Robb "has a lot of appeal because of his Virginia success," but said he finds "his interests are a bit too conservative for me." Dark Horse for President

Others say they still know of Robb principally through his marriage. Jo Murphy, a Michigan Democrat whose organization recently invited Robb to speak in Grand Rapids, said she knew little of Robb's accomplishments except for the recent elections. His marriage "was the first thing that popped into my head, but I shouldn't say that," she said.

Many Democrats rate Robb, a stern-faced lawyer and former Marine combat officer, as a dark horse for president. He is more frequently mentioned as a vice presidential candidate, as much for his term as governor as his ties to Texas and growing concern that the party may need a moderate southerner to be competitive with the GOP and to help forestall political realignment in the region.

Robb, who will practice law in Virginia and live in McLean, characteristically has left his plans vague. He is, however, doing little to dissuade supporters who are encouraging him.

He shows no signs of easing the hectic schedule of speaking engagements that have taken him across the country and has vowed to keep up his sometimes controversial efforts to move the national Democratic Party toward a more moderate image. "For personal reasons" he has said that he will focus more on national defense and foreign affairs issues after he leaves Richmond.

As governor Robb played a role that has taken him out of Virginia frequently, heading at various times the Southern Governors Association, the Democratic Governors Association, the National Governors Asociation, the Education Commission of the States and a host of other lesser known organizations.

"Chuck Robb has a pretty good idea where he's going," said David Doak, the Washington consultant who helped manage Robb's 1981 gubernatorial campaign. Doak, who is currently working for Delaware Democratic Sen. Joseph Biden's exploratory presidential efforts, acknowledged that even he has had difficulty discovering what Robb's plans are.

"If Robb were running, he would have kept Doak to himself," said one Robb appointee who is skeptical about the governor's national intentions. The official, who asked to remain anonymous, argued that Robb needs to increase his visibility quickly now that Sen. Edward M. Kennedy has decided not to run for president.

"We can catch up just as quick as we want to . . . . The network is there to raise the money and we wouldn't be able to cut the spigot off," said Virginia Del. Alson Smith, a Winchester businessman and longtime fund-raiser for Robb. "The door is more open in the last 30 days than it has been in the last four years."

Smith said Robb "isn't out seeking the nomination, but he's out doing what he thinks is right for this country. If the time comes he feels he wants to run , he'll let us know."

Even under federal campaign laws, much stricter than those in Virginia, Smith said Robb could quickly raise $2 million -- more if he were to decide to establish a political action committee that promoted several candidates. Danger of Declaring Early

Smith said Robb could defy conventional wisdom and wait another year before making up his mind, and could benefit as a strong regional candidate if more than a dozen southern states go through with plans for a one-day southern primary in early 1988.

"One of the things I've heard him say over and over again is that he feels like politicians get out too early . . . . The longer you're out there, the more they have a chance to bite at your ankles," said one Robb staff member in Richmond.

Robb has said he will remain active in the Democratic Leadership Council, a moderate group of mostly southern and western state elected officials that Robb helped organize, through the 1988 elections.

The group has given Robb national exposure. Hadley Roth, a veteran Northern California political organizer and adviser to San Francisco Mayor Diane Feinstein, said the DLC, including Robb, had made a good impression in a recent swing through the West.

"We are future-oriented," Roth said, suggesting Robb needs to get more national attention. "There's no simple way. Personally, he would be the kind of attractive, younger politician who would have promise out here."

In between the euphoria of Robb's victory four years ago and the 1985 Democratic sweep, Robb has suffered some lean periods and low points that have caused some to question his extreme caution and political acumen:

*Immediately after his 1981 victory, Robb, without announcing it, converted $200,000 in leftover campaign contributions to a political action committee, only to abandon it when he was accused of creating "Chuck-PAC," a political slush fund.

*Virginia Democrats fumbled a chance in 1982 to capture the open Senate seat held by Harry F. Byrd Jr. and his father for five decades, after a little-known legislator handpicked by Robb and other party leaders withdrew from the race. Robb then declined to help select a candidate and complained after the nominee's defeat that the Democratic nominee lacked enough "fire in the belly" to win.

*In 1984, Robb discouraged so many candidates who wanted to run against GOP Sen. John W. Warner that the governor was accused by some of favoring Warner, a contention Robb's critics say he has yet to fully answer. The party ended up with former Norfolk legislator Edythe C. Harrison, who was trounced 70 to 30 percent, with Robb offering her only minimal support.

*In 1984, Robb backed Ohio Sen. John Glenn for president just days before Glenn's campaign collapsed. In the spring, when Walter F. Mondale appeared to be headed for the nomination, Robb, then chairman of the Democratic Governors Association, launched a book-writing project by the DGA on critical issues. The book was targeted for release after the election, which some say was an indicator that Robb long believed that Mondale would lose.

*A year ago, Robb led a highly publicized but unsuccessful national search for a moderate candidate for Democratic National Committee chairman to oppose Paul Kirk, a close associate of Kennedy, who won the job. Kirk subsequently was critical of Robb's leadership council, but the two men appear to have reached an understanding and now speak highly of each other.

*Some party leaders in Virginia say Robb has ignored local Democratic officials in his appointments and say he carried his nonpartisan approach too far for a party that had won the governor's mansion after a 12-year drought.

*Known for his circumlocution in answering simple questions, Robb has joked privately that he has "raised obfuscation to an art form."

Robb also is noted for his caution, sometimes taking it to a ridiculous degree. In his 1981 campaign, Robb stopped by a Portsmouth barbershop and remarked, "Well, I have never used a hair dryer myself [long pause]. . . but I don't have anything against those who do."

Even as a child, Robb's mother said recently, he was so deliberative and cautious that some family members and friends called him "the little ol' judge." Robb himself says that he is sometimes cool and aloof and disdains the backslapping nature of politics that often plays a key role in establishing bonds with other politicians and supporters. Labor Leaders Skeptical

Robb's fiscal conservatism and moderate image on social and labor issues, however, has won him skeptical reviews from state and national labor leaders.

"Based on the general tone of what his administration has sounded like, I'd have to regard him as well down the list," said William W. Winpisinger, liberal leader of the International Association of Machinists and Aerospace Workers.

Winpisinger said Robb was among several Democrats "running around the country . . . who sound a lot more like Republicans than Democrats."

Danny LeBlanc, secretary-treasurer of the Virginia AFL-CIO, praises Robb for "opening doors to labor" in the state, but resents Robb's reference to labor as a special interest. Robb, who has courted assiduously state and national business leaders, doesn't "have a problem flying around in corporate jets and attending corporate functions," LeBlanc said. "If that's not a special interest, I don't know what is."

Nationally, Robb has been an unabashed supporter of military spending and President Reagan's basic goals in Central America. Robb also has called for Congress to tie together tax reform and deficit reduction to make each more acceptable and to include all programs -- defense as well as such Democratic issues as Social Security -- in the budget belt tightening.

"If the Democratic Party is viewed simply as the spokesman for the have nots, it's going to be very difficult to ever attract a critical mass of voters . . . ," Robb recently said to political reporters in Washington. "But that's different from saying we ought not to associate at all" with such programs or with politicians who espouse them.

Robb has aggressively pursued affirmative action in Virginia and earlier this year in a strongly worded speech in Illinois, said it was past time for the Reagan administration to enforce the nation's civil rights laws more aggressively.

The governor has been surprisingly direct in playing down speculation he would run in 1988 against freshman GOP Sen. Paul S. Trible, disdainfully describing much of the work of the Senate as having no beginning and no end. Nor does he want to run for governor again in 1989 -- fearing any second term inevitably would be compared to his very successful first.

"I think clearly the governor has been an agent of change who has moved Virginia not just to leadership in the South, but in many ways in the nation, and you can't duplicate that" in a second term, said George M. Stoddart, Robb's press secretary.

"He hasn't expressed to me that he's planning to run" for national office, said his wife Lynda, who many -- including her mother, Lady Bird Johnson -- praise for putting aside her initial distaste for Robb's decision to enter politics. "He's going to make that decision himself . . . . I've asked him , just like you have," Lynda Robb said.

"Chuck has established his own identity very well . . . ," she said. "I'm sorry my father never saw him in elective politics. It would have pleased him very much . . . but maybe it would have been more difficult."

"It was a clear advantage . . . a big plus," Robb said recently of his marriage, which gave him a jumpstart on a political career that began in 1977 when he successfully ran for lieutenant governor in his first campaign for elective office.

He insists, however, that President Johnson's liberal Great Society handicapped him in confronting conservative Virginians. Had he failed, Robb said the derision would have been as great as his current plaudits.

"If you make anything less than a thorough impression, regrettably that can be remembered, too."