When Virginia State Sen. Nathan H. Miller stepped before the cameras at a Richmond press conference earlier this week with a cadre of GOP notables, he was hoping to present an upbeat picture of his campaign for lieutenant governor.

Instead, for the third time in as many weeks, the Republican nominee's press conference was dominated by sharp questioning about what Miller acknowledges as an "apparent conflict of interest" in drafting and voting for legislation that has given his legal clients, the state's electrical cooperatives, $13.2 million in tax breaks and business advantages.

"It has obviously had an adverse effect on (Miller's) candidacy. There's no question about that," said state Sen. Wiley F. Mitchell, one of Miller's campaign advisers. "He's going to have to work doubly hard to offset it."

Along with all the furor has come what many say is renewed interest by legislators in strengthening the state's conflict-of-interest laws. Virginia law does not presently prohibit lawyer-legislators like Miller from voting on bills that may affect themselves or the clients they represent.

"I think this will help (promote) ethics legislation," said state Sen. Adelard L. Brault (D-Fairfax), who last year unsuccessfully sponsored an ethics bill. "When something like this occurs, it has a bad flavor to it and I think there's enough people here who want to make sure it won't happen again."

Miller, a Rockingham County Republican, insists that he has done nothing wrong in promoting and voting on his clients' legislation, and says behavior like his is not unusual among the state's 140 legislators.

Spokesman for Miller's running mate, Attorney General Marshall Coleman, maintain that the details of Miller's dual role, which were first reported in The Washington Post, have not substantially hurt the Republican effort.

They cite a recent poll conducted by two state television stations, which found Miller trailing his Democratic opponent, former Portsmouth mayor Richard J. (Dick) Davis by only two percentage points, with 47 percent undecided. Coleman was reported trailing his opponent, Lt. Gov. Charles S. Robb, by three percentage points, with 28 percent undecided.

"I think Miller has stumbled a bit, but I don't think it's anything permanent," said Coleman press secretary David Blee. But Republicans in the Miller organization say many campaign workers are demoralized by the controversy.

Because the state's No. 2 job is largely symbolic and there are fe issues to debate, they say, Miller has had no other issues to deflect public attention. "This is the kind of thing that could be a death knell when it doesn't have to be," said one GOP adviser. "If he could only get off that and onto something more positive."

Miller appeared to be trying just such a strategy yesterday, when he publicly criticized Davis for supporting former President Carter's decision to move repair work on large aircraft carriers from Newport News to Philadelphia. That decision, Miller said, cost Virginia's Tidewater area 2,6000 much-needed jobs.

Several earlier efforts by Miller and Coleman to steer clear of the conflict issue proved unsuccessful. Miller's Richmond press conference this week went out of control when former Gov. Linwood Holton mentioned the conflict charges and repeated Miller's contention that he had done no wrong. The comment sparked 15 minutes of questioning from the Richmond press corps, and steered the meeting away from the subject Miller wanted to discuss: the formation of his campaign steering committee.

"I came here to give you my organization . . . I hope that's the headlines for tomorrow," said a clearly uncomfortable Miller.

The same thing had happened to Coleman last week when he held a press conference to announce a political appearance by President Reagan scheduled for Sept. 24.