With just 20 days left before the Nov. 4 election, District of Columbia Republicans yesterday got around to opening a city headquarters for Ronald Reagan and George Bush. Despite the lateness of the hour, they included the requisite ribbon-cutting and optimistic claims of victory.

Most national polls have already put the District's three electoral votes securely in President Carter's column. Reagan's appeals to blacks and to bluecollar workers now seem unlikely to overcome the city's formidable statistical obstacle -- Democrats here outnumber Republicans 202,298 to 23,005.

So Reagan-Bush campaign officials here privately concede that they would consider it an impressive showing if the Republican presidential ticket in the District wins more votes than conventional wisdom now suggests that it will -- more than the 22 percent Richard Nixon got here in 1972 and more than the 17 percent Gerald Ford won in 1976, when both those Republican candidates were incumbent presidents.

"I think we will come out as high as 25 percent," said Melvin Burton, the lawyer who is cochairman of the campaign here.

The key to winning the District is to carry the city's overwhelmingly black majority, political observers agree, and this year Republicans are counting on black disillusionment with Carter's economic policies to produce a stampede of black support to Reagan.