Just a few months ago, some Northern Virginia Republicans were saying that Rep. Frank R. Wolf had written off his chances of carrying Arlington in the fall elections.

While the three-term Republican congressman's chances of capturing what has been one of the state's most solidly Democratic counties remain slim, it is clear that Wolf is determined to prove the naysayers wrong.

It was Wolf, for example, not county officials, who announced what was going to happen to a major county traffic headache -- the George Washington Parkway approaches to the Roosevelt Bridge. He has expressed concern on other issues that have preoccupied the County Board in recent years, such as keeping grocery stores in redeveloping areas and promoting the creation of a day care center in Crystal City.

"The congressman is not only not 'writing off' Arlington, but he fully expects to carry Arlington," said Ed Newberry, a spokesman for Wolf, who is not formally announcing his candidacy until May 19.

Carrying the county will be a difficult goal this year because Wolf's Democratic opponent is certain to be Arlington County Board Member John G. Milliken, the most popular vote-getter in recent county history.

A former top aide to Rep. Joseph L. Fisher, whom Wolf defeated in 1980, Milliken has also gained recognition from his day on Capitol Hill and as the former chairman of the Metro transit board.

With about 30 percent of the voters in the 10th Congressional District, Arlington has not been pivotal in recent elections, but this fall could be different, according to Milliken supporters. They are hoping for a high turnout in Arlington and a lower than normal vote in Loudoun and northern Fairfax counties and the cities of Falls Church and Fairfax City, where Wolf has been strong.

Ultimately, the Milliken-Wolf contest probably will be decided in Fairfax County, where 55 percent of the district's voters live, voters most responsible for Wolf's impressive victory margins in his last two campaigns.

They are also fiercely independent voters who will swing to Democrats as they did last year when they helped sweep Gov. Gerald L. Baliles and the rest of the statewide Democratic ticket into office.

If early predictions of a light turnout materialize in Fairfax and elsewhere in the district, Wolf will need to cut into any home town edge Milliken may have in Arlington.

In 1984, when both candidates were last on the ballot together, Milliken won reelection to the County Board by an unprecedented 70 percent of the vote. Wolf also captured Arlington for the first time, winning 54 percent of the vote.

Milliken outpolled him by 4,000 votes in that presidential election year. Such a margin is not likely to be repeated in this off-year election, but Wolf supporters say they need to guard against Milliken's running up a significant edge in Arlington if there is a light turnout elsewhere.

"We fully expect to carry Arlington by a wide margin," said Patricia B. Carroll, Milliken's campaign manager. "Not only do we have an organization in place, but we have a candidate who has carried Arlington by the greatest margin in any Arlington election in history."

Milliken's forces, backed by a formidable Democratic county precinct operation, are gearing up to blitz Arlington and to help elsewhere. Their task was made easier last week when county Republicans announced they do not expect to field candidates in the local elections for County Board and prosecutor. That decision should free the usual army of Arlington Democratic volunteers to work for Milliken elsewhere in the 10th District.

Arlington Republican leaders say they did not exert pressure to get candidates because they said they want to focus all their energies behind Wolf.

Their first priority will be to shore up the GOP's weak precinct organization, the reason one person cited in his decision not to run for the County Board. "It certainly needs strengthening," agreed Edna Johnson, Wolf's Arlington coordinator.

Some Republicans say they believe Wolf's campaign is kicking off earlier than usual. Charles White, who is managing his second Wolf campaign, disputes that.

"I don't think we're starting any earlier," he said. "But we may be starting a little smarter in Arlington this time . . . . We would like more people in Arlington to meet Congressman Wolf."

White said the campaign recently conducted a poll in the district. Both he and Wolf's office declined to disclose the results or to characterize them.

Perhaps the most recent example of Wolf's determination not to be bested by Milliken involves an abandoned county plan to build a police station on land the county expects to get at federally owned Arlington Hall.

Citing citizen opposition to the station plan, Milliken asked that other sites be explored. Days later, thousands of county residents received letters from Wolf reminding them of his role in the issue and how he had intervened on their behalf to keep the station out.