In a city where big-time politics is commonplace, it still comes as a shock to many people that Washington locals have the audacity to try to land the 1984 Democratic National Convention. The funny-hat brigade has always gathered somewhere "out there" in the country, not in the bosom of the bureaucracy.

But undaunted city officials and business owners are vigorously pitching Washington as the ideal site. Last week, they gave the VIP treatment to the Democrats who will decide where to stage their party's next nominating gathering.

Democratic Site Selection Committee members, who were whisked about Washington's lively new Convention Center and treated to a lavish reception in their honor, expressed polite admiration for the city's ambitious bid for the convention.

Washington is "nice," as one committee member put it, but many Democrats were gazing westward to San Francisco as the probable spot to anoint the next Democratic presidential nominee.

National Democratic Party Chairman Charles T. Manatt, a Los Angeles attorney, is said to prefer that California city, which is making an aggressive bid. Washington officials are less worred about competition from Chicago, New York and Detroit--the only other cities in the running. The choice officially will be made April 28, after as many as 60 committee members and advisers tour the cities.

City leaders are tantalized by the prospect of landing an event that could pump an estimated $20 million into the local economy.

Even if their chances are slim, D.C. officials see the bid for the Democratic convention as Washington's maiden voyage into big league competiton for major events. At a minimum, the bid will provide the city with considerable national exposure and experience that will help it go after future prestige bookings.

"It's a natural," Deputy Mayor Ivanhoe Donaldson said again and again as he worked the Convention Center reception last week.

The new $100 million, 800,000 square-foot Convention Center, which opened recently, has become the city's equivalent of those giant "Respect" buttons worn by Redskins fans.

After years of complaints that the cash-short District has done little to capitalize on its unique array of tourist attractions, local officials and businessmen now are begining to talk of unlimited opportunties for attracting convention trade and tourism to boost the economy.

On paper, at least, city officials makes a strong case for the Democrats holding their next convention here.

The D.C.-based Democratic National Committee would save a small fortune in moving costs, office rentals and hotel accommodations by remaining here. A large number of delegates, including all Democratic members of Congress, likewise would be spared the cost of travel. The city has roughly 37,000 hotel rooms inside the Beltway, and most are located near Metro or bus lines.

Moreover, the argument goes, Washington is the communications capital, with more than 3,000 accredited reporters stationed here. Television networks have major headquarters here and the Democrats would be assured of getting prime-time coverage because Washington is in the eastern time zone.

Finally, officials say, Washington could assure the Democrats unsurpassed security for their convention, with the help of the Metropolitan Police Department and the National Park Service Police, who have considerable experience handling large crowds.

But from a political standpoint, Washington's case seems much weaker.

For instance, the last two Democratic conventions were held on the East Coast, in New York City. Democrats from the Sunbelt and western states are arguing, with some validity, that it's their turn.

Moreover, for political strategists who still believe--in the Age of TV--that a key state or region can be won by holding a national convention there, then California, with 45 electoral votes, is far superior to Washington, D.C., which has only with three.

But the "fun factor" also cannot be discounted in the final decision. Quite frankly, a lot of delegates--and media representatives, too--believe it would be more fun to meet in glamorous San Francisco, where the weather is likely to be pleasant, than to stay at home in hot, humid Washington.

Some political insiders believe Chicago may have a shot at the convention--but only if incumbent Mayor Jane Byrne is defeated by challenger Richard Daley Jr. or Rep. Harold Washington in Chicago's Democratic primary Feb. 22. National Democrats are reluctant to gather in Chicago as long as the abrasive and unpredictable Byrne is calling the shots.

Whatever the outcome, some influential Democrats say the city at least has positioned itself for making a strong bid for second prize: the Democrats' 1986 mid-term convention. That is more realistic, even some city officials agree, but, for now, they say they aren't running for the vice president of political conventions.