Virginia State Sen. Wiley F. Mitchell stood in an Alexandria pub last week under a halo of paper shamrocks, regaling a crowd of local Republicans. "I'm resurrected," he crowed. He was talking about the grueling final days of the 1982 legislative session, but he might just as well have been referring to Alexandria's once moribund Republican Party.

The party has come a long way from the days when people looking for its headquarters were directed to an Old Town telephone booth. Fifteen years ago, Republicans had not elected a candidate to Alexandria city hall in more than a century. Today, three out of seven City Council members are Republicans, including Vice Mayor Robert Calhoun.

Calhoun, a Washington attorney, is the city's first Republican mayoral candidate since Reconstruction, and on May 4 will lead a slate of six candidates in an unprecedented challenge to the city's Democratic Party. Calhoun has taken to issuing what some call brash debate challenges to Democratic Mayor Charles Beatley, and city Democrats acknowledge that this year they have a fight on their hands.

"We feel challenged," said Beatley, a retired airline pilot. "We could lose as easily as win this if we didn't work hard. Fortunately, we've got a lot to work with." That was a reference to the Reagan administration's cuts in federal funds to cities, which some Democrats see as their greatest campaign weapon this spring.

"What will tip it is whether people want to change the style of government that we have," Calhoun says. "I think they do. Chuck Beatley has become kind of an institution."

The Alexandria Republican Party didn't rise overnight, and tilting at city institutions is what has made the party. Capitalizing on the city's rapid growth in the early '60s and the declining power of city Democrats aligned with the Byrd organization, a handful of Republicans worked doggedly for a decade to make being Republican more than just a state of mind.

They found their base in the Alexandria's West End--the area between Shirley Highway and the railroad tracks--which in the 1960s had begun to fill up with young couples and families whose presence was transforming the sleepy southern town into a city. The newcomers formed civic associations, went to PTA meetings and scrutinized city hall. It was there that they collided with established Alexandria -- the city with a statue of a Confederate soldier at one of its busiest downtown intersections.

"I think we all felt we were being denied access," says Mitchell, a North Carolinian with Democratic roots who came to Washington in 1964 to work for the Southern Railway System.

There were few options then for Alexandria's politically ambitious. "You signed up with the Byrd machine, you did the functionary jobs, and you waited," recalls George Cook, a Washington parking company executive, who, with Mitchell, joined the Republican ranks. "The Democrats were complacent. The idea was 'You want to join the Democratic Party? Fine. You don't want to join the party? That's fine, too.' "

In the meantime, a few Republicans were working the neighborhoods. "Our biggest selling point was the advantage of two parties," says City Council member Carlisle Ring, a lawyer from New York who came to Alexandria in 1956 and has shepherded the GOP ever since. "We'd tell people that it was just like grocery stores. With competition, you don't get taken for granted."

Every Monday night, a dozen Republicans armed with poll tax lists set out into the Democratic wilds. Fortified with coffee, they canvassed the precincts, peddling the party line.

"I don't think there was one door in the city that I hadn't knocked on," Ring says. And every knock was recorded: blue cards for Republicans, pink for independents, and white for Democrats or undecideds.

By 1964, the Republicans' precinct work began to pay off. The party offered its first candidate for a local election. He lost. But in 1967, Mitchell ran for City Council -- and won. By then, the Republican National Committee was helping the local party with seminars and polling advice.

While the GOP was gaining a foothold, a new crop of Democrats, products of the city's increasingly active civic associations, was mobilizing to wrest power from a Democratic City Council that the civic groups believed was letting high-rise developers run away with city hall. Beatley was elected mayor in 1967, after spending a decade fighting zoning battles. But many of the city's offices remained controlled by Byrd Democrats.

In 1977, the Republicans, with the help of lobbyists for the Equal Rights Amendment, astounded many by defeating Alexandria's longtime Democratic delegate, James M. Thomson, who was in line to become chairman of the House Appropriations Committee. The GOP's rookie candidate, Gary Myers, not only trounced Thomson, he also outpolled the other Democratic incumbent.

Though the victory is generally attributed to Thomson's anti-ERA stand, former GOP chairman Nancy McCabe attributes the win to Myers' courtship of condominium owners in the West End. "Condominiums were a new thing to the city. We knew the condo owners had just formed a study group, and we went after them."

Mitchell went to the state Senate in 1975, knocking off Leroy Bendheim, a former mayor and Demcratic power broker. Drawing on both Republican and Democratic support, Mitchell ran unopposed in 1979. Mitchell and his party have also benefited in the revitalization and expansion of Old Town, the city's historic center. The neighborhood's refurbished row houses and new town homes attracted affluent residents who have swelled Republican ranks.

Gone are the days, says Ring, when local businessmen, reluctant to betray the Democratic establishment but sympathetic to the Republicans, would make clandestine drops of postage stamps to further the GOP cause.

Virginia voters do not register by party, so there is no official count of how many of Alexandria's 45,659 voters are Republicans. The GOP still had to scramble to field a full council slate this year, while the Democrats had nine people who wanted to be candidates and eliminated three of them at a mass meeting.

Joining Beatley are two Democratic incumbents, attorney Donald Casey and stockbroker James Moran; also running are accountant Lionel Hope, the only black candidate in the race, job counselor Richard Leibach, PTA activist Patsy Ticer and lawyer Mark Pestronk.

The Republicans candidates are incumbents Ring and Marlee Inman, a former aide to Beatley, and newcomers Janet Wilson, a computer manager; Robert Gardner, a retired government administrator; Washington attorney Gene Lange and William Glasgow, a management consultant and retired Army colonel.

"I think it takes a lot more courage to run as a Republican," says the GOP's McCabe. "This is still a Democratic city." Others say the majority of Alexandria voters are independent, voting for the man, not the party. Democrats, in public at least, brush the Republican challenge aside like so much sand from their shoes.

"The Republicans have never consolidated their gains on the council," said Democrat Casey. "They tend to test the water on both sides of an issue and then hang back to feel the prevailing political winds. These are the people that sent Ronald Reagan to Washington, and the people of this city know that."

"How seriously are they taking us?" asks Republican Ring. "Generally, I've heard they're pretty self-confident. They've just come off a big win." That was last November, when the city's incumbent Republican delegate to Richmond was defeated and Alexandria sent two Democrats to the capital along with Democratic Gov. Charles S. Robb.

Beatley remains popular, the Republicans concede. Lured out of retirement in 1979 by a group of Democrats and Republicans as the only moderate strong enough to recapture what was felt to be an unresponsive city government, Beatley got much Republican support last time. This time, however, many feel those Republican votes will go to Calhoun.

"Many people in this city have known Bob and Chuck for a good many years," says Republican Inman. "They go to the same church, they have the same friends. This one won't be easy for anyone."