About 175 Virginia Democrats spent last Friday at the White House, listening to President Carter and his top advisers extol the accomplishments of his administration.

It was the latest example of how the Carter-Mondale reelection team is out-organizing and out-recruiting the presidential campaign of Sen. Edward M. Kennedy (D-Mass.) in the scramble for the support Washington-area Democrats.

"It's an all-expenses-paid day" of politicking, sneered Ernest Kessler, Virginia coordinator of the Kennedy-for-President commitee, of the White House affair for Virginia Democrats, one of 18 "state constituent briefings," according Carter officials. Maryland Democrats were at the White House on Nov.1.

Kessler is wrong about the expenses (the Democratic National Commitee picked up the tab for the buffet lunch, but participants provided their own transportation), but he is right about the politicking.

And the briefings are getting results. George H. Gilliam, the Charlottesville lawyer who is Virginia coordinator of the Carter reelection drive, said he counted several converts to Carter after last week's meeting.

Although no local Democrats were injured in a rush to jump aboard the Carter bandwagon following the president's formal announcement of his candidacy a week ago, Kennedy's earlier announcement reaped even fewer commitments from local party leaders.

The majority of them are reluctant to take sides, at least this early, in a family fight. But among those who have, most -- including D.C. City Council Chairman Arrington Dixon, Virginia Lt. Gov. Charles S. Robb and Montgomery County Executive Charles Gilchrist -- have picked Carter over Kennedy.

Kennedy has picked up endoresments from three members of the D. C. City Council, Betty Ann Kane, John, both at-large members, and Nadine P. Winter of Ward 6, about half of the D.C. state Democratic committee and two key members of the campaign staff of Mayor Marion Barry, treasurer Max Berry and strategy chief Joseph B. Carter.

The mayor hasn't declared his choice, but Barry has shown up at several Carter fund raisers in the city, And the president has the official endorsement of D.C. State Chairman Robert B. Washington Jr.

Support for the president among city officials may be as shallow as Rock Creek before a spring rain, however. Whoever is in the White House is important to the District government because its budget required approval of the president's Office of Management and Budget. So a District mayor has little to gain by picking a fight with a president, even though, as liberal lawyer Joseph Rauh declares, "Carter couldn't beat Kennedy in the District if Abraham Lincoln were his campaign manager and Thomas Jefferson his treasurer."

County Executive Gilchrist held a party at his house to watch Carter's announcement, but a poll of Montgomery County's Democratic Central Committee two months ago showed Kennedy the choice by 12 to 2. County Chairman Stanton J. Gildenhorn, who endorsed Kennedy last May, believes the Carter-Kennedy race "will not be divisive" in his suburban jurisdiction.

The Democratic establishment in Maryland is titing heavily to Carter, with Baltimore City Council President Walter Orlinsky the biggest name in Kennedy's camp. Gov. Harry E. Hughes will make his choice known "in my own time," but he has said he is pleased with most of the actions, policies and directions of the Carter Administration. Others leaning to Carter include State Party Chairman Rosalie Abrams and most of the legislative leadership.

There is no detectable support for the third Democratic candidate, California Gov. Jerry Brown. Even though Brown beat Carter in the Maryland primary in 1976, Rep. Michael D. Barnes said, "I know of nobody in Montgomery County Democratic circles who supports Brown."

Across the Potomac, Northern Virginia Carter coordinator Lynne Johnson, who also is the Democratic chairman of the 10th Congressional District, conducted a survey last weekend and found "lots of Carter support," including that of state senators Adelard L. Brault, Clive L. DuVal 2d, Edward M. Holland and Charles L. Waddell and Fairfax County Supervisor Martha Pennino.

Gilliam, the statewide Carter coordinator, believes Carter has the lead in Virginia, but cautioned that "Lloyd Bentsen [the Texas senator] had the most endorements in Virginia at this time four years ago, and he didn't get a single vote." Just because he hasn't seen a lot of Kennedy support does not comfort Gilliam, who noted, "the guys on the Titanic didn't see a lot of ice either."

The only local member of Congress from the area who has announced an endoresment is Maryland Rep. Beverly B. Byron of Frederick, who picked Carter two months ago and thinks her choice is "looking better every day."

But because all members of the House are up for reelection themselves next year, most see little political benefit in making a choice this early among presidential hopefuls.

"I made a pact with the voters," grinned Rep. Herbert E. Harris Ii of Fairfax, "I take on the heavy responsibility of legislating, and they get to pick the president."

Asked which man's philosophy he admires the most, Rep. Joseph L. Fisher of Arlington answered wryly, "I don't regard either of them as philosophers."