For Fairfax County Republicans, Plan A was this: Spend a year to find and persuade just the right opponent to take on Katherine K. Hanley, the county's top Democrat, chairman of its Board of Supervisors.

The result of the effort? Someone had to invent Plan B.

First one, then another, and finally all of the rising stars in the local Republican Party considered and ultimately nixed the idea of taking on the politician known across the county as just "Kate." The June deadline for naming a GOP opponent came and went, leaving Hanley facing a Libertarian and two independents, but no Republican, in November.

That leaves Plan B as the GOP heads toward election day, a decision to ignore Hanley altogether and concentrate on winning seats on the board in districts where Democrats appear weakest, thus stripping Hanley of the one real power she wields: her majority.

"We just view it as another way of taking control," said Republican Chairman Joseph Underwood, "to go for the majority or a deadlock--to make Kate the 'Queen of Nothing.' "

How did the Republican Party in Virginia's largest jurisdiction fail to offer a candidate for the county's top job at a time when the GOP holds all three statewide offices and is on the verge of a historic takeover of the General Assembly?

Fairfax politicians and business and civic leaders say it's largely a reflection of the booming economy and Hanley's ability to position herself to take credit for it. Hanley, a former teacher with an encyclopedic knowledge of the county government, has cultivated a reputation as a centrist, befriending executives of the emerging high-tech sector as well as slow-growth proponents, neighborhood activists and ordinary citizens.

Republicans contend that Hanley has offered little in the way of a vision for the future in her nearly five years as chairman. But the party's strategists, and those who briefly considered challenging her, admit she is reaping the rewards of a county whose residents are, by and large, satisfied.

"Obviously, there's a lot of things going well in Fairfax County," said Todd Stottlemyer, an executive at the high-tech firm BTG and one of those who was approached to run against Hanley and quickly said no. "You have to look at the overall economic situation. Are people generally happy? When people are happy and the economy is strong, there's very little desire for change."

Making the search for a challenger more difficult was that the two issues dominating election-year headlines, transportation and education, are only minimally the responsibility of the board.

"Kate's obviously viewed as a very strong incumbent," said William Hazel, a surgeon who was approached about taking on Hanley. Hazel, nephew of prominent developer John T. "Til" Hazel, said Hanley has "managed to not become unnecessarily controversial, so it doesn't leave an easy wedge for people. If you had a big, biting, driving issue, you might be able to do something."

Sully District Supervisor Michael R. Frey wavered for months, in the style of Mario Cuomo, before deciding not to challenge Hanley, saying he decided that raising money would be too difficult.

The chairman is the only member of Fairfax's 10-seat board who runs countywide--the others are elected by district--which makes that campaign far more expensive. Republicans estimated that it would take $500,000 to run against Hanley and that, given her popularity, the money would be better spent on district races.

"How are you going to raise the money to spread the message?" Frey said he asked himself before deciding to run for his current seat again. "There's clearly a limit on resources," he said of the county party. "You don't go throwing the resources away on unwinnable races. If you are not going to run a serious candidate, there's no reason to waste [money]."

That doesn't mean the Republicans will go soft on Hanley in their rhetoric. Frey said the chairman has contented herself with the minutiae of government at the expense of sketching grander plans for the county, and has used the good economy as an excuse for maintaining the status quo.

"The only thing I will give Kate credit for is knowing how to stay out of the way," Frey said.

Hanley wouldn't say publicly why she thinks the Republicans aren't challenging her. Asked whether she felt lucky, she answered: "I'm a great believer in luck. The harder I work, the more I have of it."

But she did call criticism such as Frey's unfair. Under her leadership, she said, the county has expanded funding for education, increased its police department, streamlined agencies, started revitalizing older communities through tax breaks and begun to reinvest in public works such as sidewalks, streetlights and trails.

Hanley acknowledged that hers is a low-key, low-profile approach--in contrast to some of her predecessors--but said that she gets results by knowing details of the workings of county government and spending every spare moment out in the community.

Her supporters say that knowledge translates into a behind-the-scenes power that is difficult to describe--and to beat.

"I happen to believe we have a very effective leader in the chairman of the board," said Democratic Supervisor Gerald E. Connolly of the Providence District, a close friend. "Her agenda is a passionate devotion to maintaining and improving the quality of life in Fairfax, continuing to lower the crime rate, improve on the school system."

Indeed, even some Republicans give Hanley good marks. They say she is getting an easy ride this election in part because she has spent four years achieving results.

"The county is moving in the right direction. It's a good place to live and getting better," said Edward Bersoff, a Republican business executive. Bersoff, who supported Hanley's GOP opponent four years ago, said he was surprised that as chairman Hanley has supported moderate positions that the business community favors.

"She could have been far more unfriendly to business," he said. "Sometimes she even sounds like a Republican."

Other Republicans say it's more important to win a board majority than to displace the chairman.

She may be the county's top elected official--the one who sets the board agenda and has a bully pulpit to speak for Fairfax--but in the end, they know that hers is just one of 10 votes. Unlike Montgomery County Executive Douglas M. Duncan (D) or District Mayor Anthony A. Williams (D), Hanley has no direct control over local government agencies.

Currently, Hanley and the Democrats enjoy a 6 to 4 majority on the board, though the chairman often wins the votes of moderate GOP members Elaine N. McConnell, of Springfield, and Stuart Mendelsohn, of Dranesville.

The Republican strategy for this fall focuses largely on displacing two Democratic incumbents: former GOP supervisor Christine R. Trapnell is taking on incumbent Penelope A. Gross in the Mason District in and around Baileys Crossroads, and Republican businessman Robert Jones is taking on incumbent T. Dana Kauffman, who represents the Lee District in the Springfield-Franconia area.

If Republicans succeed there, they will turn the board's 6 to 4 tilt in their favor, providing they successfully weather two potentially strong challenges. Barbara Phillips, an activist who fought to save Evans Farm from development, is running against Mendelsohn in a district that includes McLean, Great Falls and Herndon. Robert B. Dix Jr., who represents Reston, Vienna and Oakton, is being challenged by former Hanley aide Cathy Hudgins and an independent, John Thoburn, whose family owns religious schools in the area.

Five other board members, three Democrats and two Republicans, are running unopposed.

Although the GOP is leaving Hanley alone, she faces three challengers on the ballot: Paul Gagnon, a Libertarian; Levi Levy, a frequent challenger and small vote-getter who is simultaneously running for several other county offices; and Arthur Purves, the leader of an anti-tax group in Fairfax.

Developer Til Hazel assumes Hanley will win another term, adding that it would have been difficult for any Republican to unseat her because times are so good.

Far from being Queen of Nothing--as the GOP's Underwood hopes--Hazel said Hanley is likely to be successful in the next four years no matter how many races the Republicans win in November.

"There are no major development issues, which have kept things gritty for 30 or 40 years," Hazel said. "She's Queen Victoria in Victorian England."