While many of the city's more prominent Democrats are scrambling about trying to figure out whom to support in the 1978 mayoral election, the chairman of the D.C. Republican Party has quietly accepted the likelihood that no one will ask to carry his Party's banner in the most significant local political campaign next year.

Party chairman Paul Hays says candidly that it is the only constructive position to take, given the past and present condition of the local GOP. The party's limited financial and organizational resources could best be utilized, he said the other day, by not running anyone for mayor or city council chairman in 1978.

"That's a realistic position. If you want to characterize it as humble, you can. I wouldn't. We are realistically about the business of trying to build a party," Hays said. "For the time begin, the role for the Republicans to play is to take sides in the in-fighting of the Democratic Partys' mayoral primary."

The years immediately preceding the coming of limited home rule to this city must have been nice ones for the District's GOP. While the appointed Democratic mayor constantly maneuvered to keep his head above water in the face of a Republican administration in the White House, the GOP was the party of not only the council chairman, but six of the nine members of the then-appointed council.

It was, indeed, a rarity in city politics anywhere. For not only was the city 75 per cent Democratic in its registration, but the city was also more than 70 per cent black in population, and Republicans have traditionally been seen as the party of the rich and the white.

In 1974, the balloting for the first elected local government in more than a century brought home some harsh - but not unexpected - truths to the local GOP. It failed to endorse a mayoral canidate and the only mayoral hopeful who bore the party label in the general election garnered only 4 per cent of the vote. Jerry A. Moore, a holdover form the appointed council, won election in his own right and was reelected in 1976. But no other Republican candidates have been elected to either the mayor's office or a city council seat.

And, as if to forecast a worse future, the number of Republican registrants among city voters has dropped by nearly 25 per cent in the past three years. Republican were 12 per cent of the enrolled voters in 1974. This year they are slightly less than 10 per cent.

Thus, what Hays hopes the party will do next year is decide to by-pass the top cityewide elections and concentrate its energy and resources on waging contests they think they can win in wards one, three, five and six. Even such a limited strategy has its drawbacks, however.

For example, the largest Republican registration in the city - and perhaps the best GOP organization - is in ward three, the mostly white, affluent section of the city west of rock Creek Park. There, One of every four voters is a Republican, and its was there that Hays, running in the July 19 special city council election, outpolled all other candidates, including winner Hilda Mason of the D.C. Statehood Party.

But the Democratic incumbent in ward three is Polly Shackleton, who is likely to face only token opposition if she seeks reelection next year. Democrats outnumber Republicans in ward three by a near 2-1 margin. So even with a strong, well-known Republican candidate - many Republicans hope school board member Carol Schwartz will be that candidate - the party would face an uphill struggle.

In ward six, the Capitol Hill and near Northeast section of the city, Republicans comprise only 6 per cent of the voters. It is Hays' own ward, but also one which he lost in the July 19 election. Democrats could be sharply divided in the contest for the seat held by Nadine P. Winter. But whether that division would carry over into the general election is questionable at this point. Hays says he would prefer not to run, and instead would like to find someone with greater name recognition, like lawyer and Advisory Neighborhood Commissioner ray Gooch, to be the GOP candidate.

No names have been mentioned yet in ward one or word five, Hays said. Nor are there yet any Republican possibilities for council member at-large. Ordinarily you need seasoned recognized names for such citywide races. And one problem the party now has is that its superestars of earlier years - John Nevius and Gilbert Hahn Jr., for example - don't seem interested in running. "There's a lot of wishful thinking that Gil Hahn might run. But I think it's just wishful thinking," Hays said. "If he got into any race, it would change the whole picture."

Like its counterparts in other areas of the country, the ranks of the D.C. Republican party have been dwindling. And like the GOP elsewhere, the local party has had an image problem that has suggested that only rich white folks are Republicans. Several times in the recent past, in fact, disgruntled GOP blacks have called the local party racist.

Hays hopes all of that has botomed out. There are more blacks inkey positions in the D.C. Republican Party, he says - including national committee-woman - and the Watergate syndrome, which hays blames for the loss of membershiop, should be all over.

"I don't think there's much possibility that the Republicans will be the majority party in the near future," Hays said. "But in five or 10 years I believe the Party will be strong enough to be viewed as a major opposition party here and a force to be reckoned with."