Northern Virginia's Democratic leaders headed off an attempt yesterday to endorse Lt. Gov. Richard J. Davis as the party's nominee for the U.S. Senate, but the movement to draft Davis appeared nonetheless to be gathering momentum.

George C. Rawlings, chairman of the party's 8th District committee, dissuaded Alexandria delegates from pushing the district's convention toward a Davis endorsement, saying the nomination battle for the seat of retiring Sen. Harry F. Byrd Jr. remains uncertain. The nomination battle broke wide open last week when Virginia Beach Del. Owen B. Pickett, who had won the approval of Gov. Charles S. Robb and other party leaders, withdrew.

"I just didn't think the convention should be stampeded," said Rawlings, a Lorton resident who was the party's 1970 Senate nominee.

Fairfax County prosecutor Robert F. Horan, who is considering a Senate bid this year, worked the crowd at yesterday's convention at Robert E. Lee High School in Springfield. None of the other likely Senate candidates was at the meeting, but delegates pushed candidates ranging from former lieutenant gubernatorial candidate Richard S. (Major) Reynolds III to former State Department spokesman Hodding Carter of Alexandria.

Davis' name, however, was the one most often mentioned. "I think the whole convention would go with him if he wants it," said Pixie Bell, a longtime Fairfax party activist.

The political jockeying came at what would have been a routine gathering to nominate Herbert E. Harris as Democratic candidate for the House of Representatives from the 8th District, which includes Alexandria, the southern half of Fairfax County, eastern Prince William County and the northern tip of Stafford County. Harris will run a rematch against incumbent Rep. Stanford E. Parris, who took the seat from him two years ago, and Harris accepted the nomination yesterday with a fiery speech attacking Parris' support of Reaganomics.

Down Interstate 95 in Occoquan, Parris held a barbecue, cooking 30 pigs for several hundred paying guests in a fund-raiser timed to take some attention away from his old foe's nomination. But Harris' unopposed nomination was overshadowed even within his party by the battle for the Senate nomination.

Horan said yesterday he has tried to speak more than once with state Sen. L. Douglas Wilder, Virginia's only black state senator, since Pickett withdrew, but Wilder had not returned his telephone calls. Wilder's threat to run as an independent helped force Pickett out of the race, and his support could be crucial to winning the backing of black voters. Horan is more conservative than Davis, a millionaire Portsmouth businessman, and several party officials speculated yesterday that Wilder would not support Horan's candidacy.

Horan said yesterday he will decide next week whether to run. He said he did not believe a "draft Davis" resolution would have won majority support at the 8th District convention, but he said that Davis' staff and supporters had been working hard around the state to promote a draft.

Hodding Carter, who was seen regularly on the nightly news during the Iranian hostage situation, was first mentioned as a Senate candidate last December, but said then he wouldn't run, according to one Alexandria Democrat. His name resurfaced when Pickett withdrew. Carter currently is traveling in Israel and is not participating in the scramble for candidates for the state convention in Roanoke next month.