Virginia Gov. Charles S. Robb, whose election in 1981 was heralded as the beginning of a revival of the struggling Democratic Party in his state, has emerged as a key player in the party's national attempt to rebuild from its debacle this year.

Robb is one of a handful of elected leaders guiding a search for a consensus candidate to become chairman of the Democratic National Committee, a continuing search that has involved private lunches and dinners in Washington and DNC strategy sessions last week at this luxury resort.

"Chuck Robb has done a tremendous job . . . of balancing a lot of egos and political agendas," said lameduck Utah Gov. Scott Matheson.

The work by Robb, a one-term governor barred by law from succeeding himself, has heightened speculation in Virginia and elsewhere that the son-in-law of the late president Lyndon B. Johnson is considering a 1988 run for the Senate or for national office after his term ends in January 1986. Robb has turned down entreaties to take the DNC chairman's job himself.

He is viewed by some as one of a few Southern politicians who could restore potentially crucial geographic and political balance to the party's 1988 ticket.

Those are possibilities that Robb, 45, plays down but doesn't rule out.

"I have no agenda beyond the end of my term," Robb said during a break in a meeting of the National Governors Association here, " but I don't want to make myself a permanent lame duck."

Matheson, who also rejected pleas from Robb and others to seek the DNC post, was one of nearly a dozen Democratic governors called together here by Robb to discuss strategy in the search for a chairman.

The choice of a replacement for DNC Chairman Charles Manatt, who will leave in January, is the first step in what the governors hope will be a more assertive role in national Democratic affairs and a more moderate approach to public policymaking to win back middle class voters.

Robb, a moderate whose election in 1981 ended 12 years of Republican domination of the governor's mansion, acknowledged that state leaders have made short-lived efforts to be more active in the DNC after national defeats in 1980 and 1972.

"There's a certain amount of skepticism," Robb said. "Elected officials have looked out for their own turf" while interest groups have run the national party. "The luxury of that kind of separation no longer exists," Robb said.

"The national party is just so much heavy baggage," Robb said, if he permits others to define the party in a way not acceptable to him.

Still, Robb, who in three years has broken the mold of Virginia leaders who mostly stayed away from national politics, contends his only goal now is to help make the national Democratic Party competitive again.

"I intend for the next year to remain active in national party affairs," said Robb, who has served as chairman of the Southern Governors Association and sat on numerous commissions on education and other issues. He is acknowledged as a successful fundraiser for the party and is currently chairman of the 35-member Democratic Governors Association.

Robb's many party responsibilities keep him both busy and visible. On Tuesday, he met with Rep. Tony Coehlo (D-Calif.), chairman of the Democratic Congressional Campaign Committee, and Maryland Rep. Steny Hoyer, Coehlo's liaison with the DNC, to discuss the DNC chairmanship.

On Wedesday, he was a speaker at a party forum hosted by the conservative Coalition for a Democratic Majority. Wednesday night, he convened and presided over a dinner of about two dozen party leaders at the Madison Hotel.

Robb, who generally prefers to operate out of the media spotlight, said he believes his latest efforts are likely to bring him a lot of criticism, as well as recognition, from party activists.

"What we are doing is bound to generate a certain amount of heat," Robb said. That heat is likely to come from interest groups that have traditionally had greater control over the party than elected officials have. Robb said he was a logical leader of elected officials because he is physically close to Washington, not up for reelection and has no immediate campaign plans.

But he also stands a chance like no other Virginia governor in modern times to gain favorable national attention should the elected leaders pull off their high profile move to change the course of the party.

On Monday, Robb will be the guest of an informal gathering of national political reporters in Washington, who will question him about the DNC on the occasion of the release of a new book on the party's future. The book, a project of the Democratic Governors Association, was authored by Robb and other Democratic governors.

It has been in the works since the spring, a clear sign to some that Robb and others believed early that the Democrats behind Walter F. Mondale were headed for almost certain defeat.

In his 1981 campaign, Robb assembled a coalition of party moderates, liberals, blacks and labor in a campaign that avoided frightening away conservatives. "Robb bucked all the trends in 1981," said Mark Emblidge, a political fund-raiser who worked for Robb as well as the presidential campaigns this year of Ohio Sen. John Glenn and Colorado's Gary Hart. "Robb has a style and a philosophy that's appealing all over the country."

But many state Democrats fault Robb for failing to exert enough leadership in 1982 and again this year when the state party lost Senate campaigns to Republicans.

In a telling news conference the day after this year's elections, Robb said Virginia's Democratic Senate candidate Edythe C. Harrison lost in part because she did not "establish credibility" by quietly building enough support for a public record before running.

"Enough people could create the argument," said fundraiser Emblidge, "that this is just the kind of building that Robb is doing right now."