Virginia State Sen. Nathan H. Miller had been walking through Alexandria's Old Town for more than an hour yesterday when he suddenly roared with delight. Someone had recognized him.

"Did the press hear that?" bellowed Miller. "He's heard of me! Tell them"

The event may have been the high point of the morning for Miller, the newly nominated Republican candidate for lieutenant govenor. A 37-year-old lawyer little known outside of the Shenandoah Valley, Miller had come to Northern Virginia with his running mates in an effort to counter accounts of GOP disunity.

Joined by members of the state's congressional delegation, gubernatorial nominee J. Marshall Coleman, attorney general nominee Wyatt Durrette, and Miller repeatedly sounded that them and heard it echoed by party leaders. "I'm the symbol of unity in the Republican Party," Virginia Sen. John W. Warner told them at a breakfast in Crystal City. "You are looking at a senator who is in office because of unity and for no other reason. This is a unified ticket. I can assure you of that."

The visit to the Washington suburbs was only one episode of a 10-day state tour for the three GOP candidates that follows a divisive state nomination convention in Virginia Beach last week.The tour runs from Roanoke to Newport News, and is aimed at getting the candidates maximum media exposure and an estimated six hours of sleep a night.

The Democratic ticket, headed by Lt. Gov. Charles S. (Chuck) Robb of McLean, drew a backhanded compliment from Rep. Stanford Parris (R-Va.) at yesterday's campaign luncheon in Alexandria's Holiday Inn. Parris said he doen't want Robb "coming into my district next year as governor and beating up on me."

Paris said the 1981 Democratic team is more formidable than the one fielded four years ago. "We can't scare them. Chuck Robb is not Henry Howell," he said. "And we probably can't outspend them because Chuck will probably get all the union funds. So we have to outwork them and outsweat them."

But Durrette, a former state legislator from Fairfax, stressed that the key to a GOP victory in November is the conservative philosophy that has been held by Republicans for decades. "Our opponents were on the opposite side of that system of values in 1980 and they will be again in 1982," Durrette said. "This year they wanted to be different, but they are not even good carbon copies."

In Richmond yesterday, Robb sought to refute charges from Republican Gov. John N. Dalton that a huge amount of out-of-state money is pouring into his mother-in-law, Lady Bird Johnson, is raising funds for him from among her Texas Democratic friends. "It doesn't happen to be true," Robb said.

Touring Alexandria yesterday morning inn a blur of dark business suits, Coleman and Miller encountered Alexandria cab driver Dan Freeman, one of several people who told Coleman that he had seen his television ads.

Freeman, who is black and lives in Fairfax, told Coleman he planned to vote for him because he has not seen much of Robb, and because Robb last year gave a speech at an Alexandria boat club that refuses to admit women as members.

But others said yesterday they weren't exactly sure what to think of the candidates, who marched up to strollers with broad smiles and ready handshakes. c"I've never heard of them before," said Nguyen Tuiet, and Alexandria Head Start teacher, as she watched Miller toss one of her preschool pupils in the air. "Which one of them is running for governor?"

The three candidates split up long enough to greet commuters at three Metro stations during the evening rush hour, at the end of which Coleman's son Sean, 11 calculated that he had passed out 950 brochures since beginning the day at 7:30 a.m.

The 14 hour sweep of Northern Virginia was climaxed with a rally last night before 400 boisterous, chanting partisans in the student union at George Mason University.

The star of the show was Miller, who said he recognized many in the crowd as among those delegates who gave him the upset nomination last Saturday night in Virginia Beach.

Durrette, speaking before a hometown audience, delivered the harshest attack of the day on the Democratic opposition. "When they figure out what they stand for, then they can ask the people of Virginia for their votes. Until then, they are little more than an organized conspiracy to seize power."

Coleman attacked Robb, saying, "They got their candidate out of the Great Society, but they are never going to get the Great Society out of their candidate," a reference to Robb's being the son-in-law of the late president Lyndon B. Johnson.