In his short time here at the Democratic midterm national party conference, Virginia Gov. Charles S. Robb managed to do just about everything there is to do at a political convention.

He met with presidential hopeful Sen. John H. Glenn Jr. of Ohio over breakfast and with former vice president Walter F. Mondale before lunch. The rest of the morning, he talked about the state of the economy and sat through a point-by-point debate over arcane policy statements.

The night before, he hit the parties: one honoring former New York Gov. W. Averell Harriman, another -- a hot-dog and hamburger-munching affair -- that was one of several sponsored by Richmond-based Philip Morris, Inc., and a small gathering to celebrate the 33rd birthday of television personality Phyllis George, wife of Kentucky Gov. John Y. Brown Jr.

At some point today, Robb managed to celebrate his 43rd birthday, an observance that harried aides squeezed into the jam-packed schedule. A surprise cake was to be presented shortly before Robb, his wife, Lynda, and two state troopers, doubling as chauffeurs headed back to Virginia so the governor could make an appearance at his 25th high school reunion at Mount Vernon.

Robb had billed his visit to the Democratic Party conference as "low key," a careful attempt to avoid the kind of splash and fanfare that could cause people to accuse him of cashing in on his celebrity status -- status that dates back to the day he married Lynda Bird Johnson, daughter of the former president.

But that celebrity status, which had helped propel Robb into office, could not be denied. Although among the Democrats' newest arrivals on the national political scene, Robb is already one of the party's better known figures.

That special status was evident wherever he went during his 24 hours here. Strangers nodded and whispered to each other when he and Lynda walked by. Television cameras, glancing over other gubernatorial couples, zeroed in on the Virginia pair.

"He's still got that celebrity attraction," said state party chairman Alan Diamonstein, one of Robb's oldest political associates. "You can see it when he walks into a room."

The Johnson family connections also have given Robb a network of Johnson family friends, many of whom would be distant acquaintances for most first-term governors. Walking into a party for House Speaker Thomas P. (Tip) O'Neill on the second floor of Philadelphia's famous Bookbinder's Restaurant, the Robbs were greeted with hugs and kisses by Rep. Claude D. Pepper of Florida, Rep. Corinne C. (Lindy) Boggs of Louisiana and others.

Not unexpectedly, all of this prompted some vague murmurings about Robb's future as a national figure, speculation that began practically the moment he was elected lieutenant governor in 1977. Robb and his top aides were quick to curb any talk of possible vice-presidential nominations in 1984, but some of the governor's loyal supporters were not so circumspect.

"I'd like to see him on the ticket," said Tom Blackburn-Rodriguez, a delegate from Fairfax County. "I think his stability and reasonableness come across really well. And as a Southerner, he would be a help for a lot of these candidates."

Vera Hall, a delegate from Baltimore who sat through the entire morning's panel discussion on "Promoting Economic Growth and Opportunity" and listened to Robb give a presentation, said she was keeping her eye on Robb. "I was very impressed with the way he was thinking in terms of long-term solutions," she said."He seems to have a particularly balancd approach."

Robb himself said later that he identifies with a group of emerging figures in the Democratic Party, a group into which he lumps Sen. Bill Bradley of New Jersey, Rep. James R. Jones of Oklahoma, Rep. Timothy E. Wirth of Colorado among others.

"I work easily with these folks," said Robb, who described the group as members of a younger generation of politicians looking for new ideas, such as Bradley's sponsorship of a simplified tax system.

"It is a group that has a clear vested interest in the future. That part I identify with I don't have to embrace every detail in the Bradley plan to applaud the idea."

Like many at the conference, Robb has decided to wait before choosing sides in the jockeying for the presidential nomination. "It is too early for me to do anything," he said. Robb said he told all the candidates mentioned that he would help them meet people in Virginia, but he made it clear that he will remain neutral for the near future.

"At some point," said Robb, "I expect I will get involved."

The star quality that surrounds the Robbs even rubbed off on perhaps the biggest political celebrity of them all at this conference: Sen. Edward M. Kennedy of Massachusetts. On their way into the governors' lunch, Kennedy hugged Lynda. And though the Robbs and Kennedy are next-door neighbors in McLean, Kennedy, amid the television cameras, turned to Virginia's First Lady and said, "I'd like you to meet my daughter."