With only a few days remaining before Tuesday's election for mayor, Republican Arthur A. Fletcher apparently has failed to attract vital support from the Democratic voters that make up the overwhelming majority of the city's electorate, according to a private poll released yesterday.

In the poll of 500 registered voters taken over the weekend by the firm of Smith Bloomingdale & Hees, only 5 percent of the registered Democrats interviewed said they would support Fletcher.

Barry holds such a commanding lead according to the poll that Fletcher could win the support of nearly all the undecided voters and still lose the election.

The poll, conducted Saturday and Sunday by telephone, shows Barry with an overall margin of 50 percent to 8 percent over Fletcher, with a huge undecided pool of 41 percent.

People with unlisted telephones were not included in the sample. For that reason and others, the poll should be considered at best a rough measure of voter attitudes.

In 1974 the Republican candidate, Jackson R. Champion got 35 percent of the total vote in the mayor's race.

Crossover voting is critical to Fletcher's chances because Democrats outnumber Republicans by a 9-to-1 margin among the city's registered voters.

The poll found that among the Democrats, 37 percent were undecided and of those undecided nearly a third said they had crossed party lines in past elections.

Even in crossovers, however, Barry did better than Fletcher. While 5 percent of the Democrats said they intended to support Fletcher, 13 percent of the Republicans said they planned to vote for Barry, the poll found.

Fletcher said he considerd results of the poll insignificant because "the greatest poll is when the voter steps behind the curtain (in the voting booth) and pulls the lever."

Florence Tate, Barry's campaign press secretary, said the poll results were inconsequential "because we know Marion Barry is going to carry 51 percent, which is the winning majority."