Less than a year ago Republicans called it the "sleeper of 1982," a chance to build on their 1980 capture of the Senate by toppling its Democratic leader, West Virginia's Robert C. Byrd.

Now, as the Nov. 2 elections draw near, polls show Byrd leading his Republican challenger, Rep. Cleve Benedict, by at least 2 to 1.

Some clues can be found in two encounters between the candidates and voters at opposite ends of the state.

As Benedict walked into a nearly empty real estate office in this Ohio River city of steel mills and recession-haunted factories, he cheerily asked the woman in charge if falling interest rates are beginning to help sales.

"What we really need is more employment in the area," she responded glumly.

As Byrd wound up a day of campaigning a week earlier in Morgantown, nestled in rolling hills near the Virginia and Pennsylvania borders, a local Republican officeholder dashed out of the courthouse to catch Byrd and invite him back for some handshaking.

He didn't like Benedict's campaign tactics, the Republican official whispered to Byrd.

Byrd, who at age 64 has represented West Virginia in the House and Senate for 30 years, faces a tougher than usual opponent in the personable, 47-year-old Benedict -- a freshman House member, former state commissioner of administration and Princeton-educated dairy farmer who is heir to the Procter and Gamble fortune.

Also complicating the race is a stridently negative campaign against Byrd by New Right activists including the National Conservative Political Action Committee and a home-grown Bye-Bye Byrd Committee, whose latest venture is a comic book that touts Byrd as a liberal and asks the question, "Are you sure he's really one of us?"

But the economy, some early campaign overkill by Benedict and Byrd's tough response to it have dimmed prospects for the upset that was once a gleam in the eye of the National Republican Senatorial Committee.

"In order to defeat an incumbent, you have to develop an issue and he Benedict hasn't done so," said Troy M. Stewart, a professor at Huntington's Marshall University, as he observed a sparsely attended Benedict headquarters rally the other day. "It's unfortunate," said Stewart sympathetically, "because he's capable."

Although Stewart and other local observers caution against overestimating the impact of the economy on the race, Benedict concedes "it's an element, no question about it." He doesn't talk much about President Reagan, who failed to carry West Virginia two years ago.

The reason is a statewide unemployment rate that's been about one-third higher than the national average. Thousands have been idled in steel mills along the Ohio River, the timber industry is in bad shape and nearly 1 in 4 workers in the coalfields of the southern part of the state is out of work.

"If the economy were better off, people would elect Benedict because they're tired of Byrd," said retiree Joseph Wilkes after running into Benedict at an autumn festival here. "But the scare is there, people are afraid . . . they're afraid of unemployment and losing their pensions, their benefits. That's why Byrd's going to win."

The economic debate has been drowned out, however, by charges and countercharges over campaign tactics.

Benedict set the tone last winter when, as Byrd kicked off his reelection effort, some Benedict supporters presented the senator with a white bedsheet with eyeholes as a reminder of Byrd's membership in the Ku Klux Klan more than 30 years ago.

Byrd responded with hard-hitting counterattacks at both Benedict and his New Right supporters, topped by a recent television commercial showing Benedict's face gradually sinking into a sea of mud.

And now a Marshall University student, with aid from a lawyer associated with NCPAC, has challenged Byrd's right to vote in West Virginia -- and thereby his eligibility to hold office -- because Byrd no longer has a residence in the state.

Byrd responds that he and his wife pay taxes in West Virginia but can't afford to maintain a home there as well as one in the Washington area. Moreover, he says, having no home in West Virginia makes it easier for him to pay visits to each of the state's 55 counties every year, a goal he usually meets, according to his aides.

The focus on Byrd's lack of a home in his home state reinforces the New Right's contention that Byrd's national role -- four years as Senate majority leader and two years as minority leader -- loosened his ties to West Virginia.

This is hard to use against Byrd, who not only spends time in West Viginia but is not shy about using his clout to get money for the state.

Benedict has disavowed NCPAC's tactics and, pelted with criticism from even some of his own supporters for the bedsheet caper, hasn't pursued the Klan theme.

But the bedsheet business, coupled with personal attacks against Byrd from the New Right, enabled the senator to set himself up as a victim of mudslinging and to come back swinging, thereby fortifying himself against suggestions that he had lost some of his earlier vigor.

Abandoning his old folksy, fiddle-playing style of politics, he made a frontal assault on both Benedict and the New Right, linking the two. Benedict doesn't like it and accuses Byrd of "using the same kind of verbiage that he accuses the radical right of using."

"They thought I'd just run back and forth across the state playing my fiddle . . . they underestimated me," responded Byrd indignantly.

But polls continue to show Byrd ahead.. The Charleston Daily Mail on Oct. 18 showed Byrd leading Benedict by 70.8 percent to 24.9 percent among likely voters.