Sensing that the odds on their long-shot bid for the 1984 Democratic National Convention have improved slightly, Washington-area Democrats and public officials rolled out a rain-soaked red carpet yesterday for the members of the Democratic National Committee who will make the final choice.

Mayor Marion Barry and members of the Washington-area Host Committee lavished food, drink and attention on the 47 members of the DNC's site selection and technical advisory committees, who arrived here in a downpour for a three-day inspection of convention facilities.

The party officials already have visited New York, Detroit and San Francisco, which until recently was the acknowledged front-runner. They also will visit Chicago before awarding the prized event on April 21. The convention will pump an estimated $20 million to $30 million into the local economy of the city that holds it.

"We started fifth, there's no question about it," Barry said at a luncheon for the DNC officials at the Washington Convention Center. "We were the last people in everyone's minds. But now we're No. 2, right behind San Francisco. We're in the big time. We're in the varsity league."

Ray Majerus, secretary-treasurer of the United Auto Workers in Wisconsin and chairman of the site-selection panel, agreed that the competition has been thrown wide open since committee members began taking a closer look at the five competitors.

"I'm not one of those who puts San Francisco as the front runner," said Majerus. "At this point, every city has an even chance. . . . I would not think that you could get the committee to make a decision today."

Many of the committee members said they were impressed with San Francisco's facilities and general ambiance. But there is widespread concern that the city's 1,900-member police force is too small to provide adequate security.

"From my point of view, that is San Francisco's biggest weakness," said Richard J. Murphy of McLean, chairman of the Technical Advisory Committee. "We told them they would have to substantially augment their police force to be considered."

Washington, which opened its new $98.7-million convention center in January, has submitted a proposal that includes $7.8 million in financial inducements to the DNC plus $250,000 to defray the expenses of low- and moderate-income delegates.

However, Murphy said the city must overcome a widespread belief that from a political standpoint the Democrats would be better off launching an assault on the Republican-controlled White House from somewhere outside of Washington.

Some DNC officials said that Barry was shrewd to give the city's effort a regional flavor by including Govs. Harry R. Hughes of Maryland and Charles S. Robb of Virginia. They said they also were pleased that Pamela Harriman, a stalwart party fund-raiser and wife of W. Averell Harriman, is chairwoman of the Host Committee.

Pamela Harriman and Barry told site selection officials yesterday that Washington is the logical place for Democrats to gather, because of the new convention facilities, a highly experienced police force, a vast array of cultural activities and the District's close proximity to about 60 percent of the delegates. Also, Washington is in the eastern time zone, which would assure that the convention unfolds during prime television time.