The embattled chairman of Virginia's Democratic Party, Joseph T. Fitzpatrick, resigned yesterday, briefly fighting tears and saying "all the winds caution me that it is time to gather my sails and trim my lines."

Fitzpatrick's surprise departure after more than six years as chairman opens up a scramble among at least a dozen potential candidates for the job of rebuilding a party with the longest losing streak in the nation.

Virginia is the only state that has failed to elect a Democratic nominee for U.S. senator or governor in more than 10 years.

Many in the party blame Fitzpatrick, a state senator from Norfolk and a leader of the party's liberal faction, for failing to build an organization to match the state's smoothly functioning Republican Party. Fitzpatrick said yesterday that "no one has asked me to resign. He said that he had decided to step down before his party's most recent defeat in the Nov. 7 U.S. Senate election.

Leading Democratic officials and office holders yesterday said that Fitzpatrick's resignation gives the party a chance to rebuild before the 1981 gubernatorial election. Sen. Adelard L. Brault, the Senate majority leader from Fairfax County called for a new chairman who can be independent of party factions.

"I think we should find someone who is not clearly identified with any particular faction, who can do the job of putting together a central committee office that is able to collect the money and provide the candidate services that the Republicans have had," Brault said. "I think those services account for 95 percent of the Republican success."

Brault did not endorse a candidate, but said he thinks there are several Northern Virginians on the list of potential chairmen. Northern Virginians mentioned by Brault and party officials include Fairfax County chairman Emilie Miller, National Committee-woman Sandra Duckworth, 8th Congressional District chairman W. Raymond Colley and party secretary John G. Milliken.

Fitzpatrick's resignation will become effective on Jan. 5, when the party's 186-member central committee meet, in Richmond to name his successor. Some Democrats hope that the generally liberal central committee will try to recapture lost conservative support for the party by naming a known conservative as chairman.

Among conservative contenders are three members of the House of Delegates, Alson H. Smith Jr. of Winchester, L. Ray Ashworth of Wakefield, and Owen B. Pickett of Virginia Beach.

Other potential candidates listed by party officials are state Sen. Hunter B. Andrews of Hampton, 7th District chairman Jack M. Horn of Charlottesvile, 6th District chairman Robert B. Lambeth Jr. of Before and 9th District chairman James P. Jones of Abingdon.

Lt. Gov. Charles S. Robb of McLean is likely to play a role in the selection but is not considered a candidate for the job. Robb is a strong contender for the party's gubernatorial nomination in 1981.

Fitzpatrick was elected party chairman in 1972 by liberals who rallied around the candidates of populist former Lt. Gov. Henry E. Howell and presidential nominee George M. McGovern. The liberal takeover that year was the climax of a fractious intraparty warfare between remnants of the once-dominant Byrd Organization and moderate-liberals who drew their strength from black voters, urban areas and organized labor.

Fitzpatrick characterized his chairmanship as an effort to build bridges between the party factions, but his image as a liberal protagonist never faded. "If bridges attract lightning then this a fact that you accept as part of your job when you are state chairman," he said yesterday. "But there comes a time when the bridgebuilding work should be passed on to someone else."