Although the final outcome of Tuesday's special D.C. City Council election will not be known until next week, it appeared yesterday that former D.C. School Supt. Barbara A. Sizemore would have to overcome steep numerical odds to overtake Hilda Mason, the apparent winner of the race.

Meanwhile, the uncertainty of the final voting results did not stop some supporters of both women from praising and taking credit for the showings their candidates had made.

"I'm eestatic because I whipped (D.C.Del.) Walter Fauntroy's, Marion Barry's and Sterling Tucker's behinds," proclaimed Council member Douglas E. Moore (D-at large), who actively supported Sizemore. "All the big Democratic guns [supported Mason] and they couldn't deal with one little me and my rag tag campaign workers. We have forged a new force. They're going to be some changes made."

Down the hall at the District Building, Council member Barry, who is Moore's arch rival on the Council, leafed through sheets of precinct results assessing how the voting had gone in places where he had actively supported Mason.

"I think Hilda did a miraculous thing," Barry said. "As she began to pick up support from the Democrats, she began to move. She's a very good friend of mine. But if she had not had the support of some of us Democrats, she would have finished third or fourth."

Statehool Party candidate Mason, who ran with strong support from many of the city's leading Democrats, held a lead of 745 votes over Sizemore early yesterday after regular ballots were counted in the race to fill the at-large Council vacancy created by the March 23 death of Julius Hobson Sr.

The contest ended in uncertainty because there are still 1,709 special or challenged ballots, at least 450 absentee ballots and 216 improperly marked ballots that will not be counted until next week.

Only after the city's Board of Elections and Ethics adds any of these 2,375 votes that are valid to the regular results can a winner be certified to complete the remaining 18 months of Hobson's term.

Mason and Sizemore are the only two of ten candidates in the race who could win depending on the distribution of the still uncounted votes.

Sizemore supporters were basing much of their optimism yesterday on the challenged ballots, which are cast whenever someone appears at one of the city's 137 polling places, asks to vote and has no registration card on tile at that precinct. Those persons are allowed to vote on a special or challenged ballot, which is counted only if the person's registration is later verified at city election headquarters.

Among several Sizemore backers, there was a belief that less than 10 per cent of the challenged ballots came from ward three, where Sizemore lost to Mason by a near 20-to-1 margin. That distribution did not appear likely, however.

Just as one of every four persons who cast regular ballots Tuesday had done so in war 1 three, nearly one-fourth of the challenged ballots were from ward three as well. If those votes reflect the same preferences as the regular ballots cast Tuesday, Sizemore would gain only about 8 votes in ward three, while Mason would pick up 149.

Outside of ward three, Sizemore ran ahead of Mason by 5- to-4 margin.If the remaining 1,307 challenge ballots similarly showed the same perferences as Tuesday's regular balloting, Mason would pick up 442 votes while Sizemore would get 545.

Thus, again because of the disproportonate importance of ward three, Sizemore's gains elsewhere in the city would be negated and she would fall an additional 38 votes behind Mason if the challenged ballots reflect Tuesday's trends.

The Sizemore supporters do not expect to pick up much ground among the absentee voters, many of whom are expected to favor Republican Paul Hays, who emphasized write-ins during his campaign. Not all of the 216 improperly marked ballots are expected to figure into the results, since many contain votes for more than one name on the ballot or for no candidate at all and are therefore invalid.

Still, optimism was ripe in the Sizemore camp. "The ball game's still open. We've got a good chance," said Acklyn Lynch, operations manager for the Sizemore organization. "We don't know the figures, but it's wide open."

Clearly, it was the endorsements and active support of three Democratic City Council members, David A. Clarke (D-one), John A. Wilson (D-two) and Polly Shackleton (D-three) that accounted for half of Mason's votes.

In most of the precincts in wards one, two and three, Democratic Party organizers worked as co-ordinators with Statehood Party members - the Democrats seeking to reach Democrats and Statehood Party members seeking their party voters and independents. Citywide, the Statehood Party has only about 1,700 registered voters.

In ward one, for example, Clarke said he got most of the ward's delegation to the Democratic Central Committee to work for Mason in his precincts. He also sent letters of endorsement to 4,000 to 5,000 ward one residents asking them to vote for Mason and to contribute to her compaign.

In ward two, Wilson also got some of his ward's precinct workers to work for Mason, including Susan Meehan, an Advisory Neighborhood Commission member and Democratic Party percinct captain.

Meehan, a long-time ward two resident who said she knows about two-thirds of the 2,000 voters who live in her precinct east of Dupont Circle, spent most of election day watching those who came to vote. Later that afternoon, after reviewing her personal file cards on voters, she sent runners to call those who had not voted, asking them to vote for Mason.

"I know everything that goes on here, I know how many white voters are here, how many black, how many young and how many old," Meehan said. "I run a very tight precinct."

But it was the ward three vote-getting effort of Shackleton and experienced political organizer Nancy Linton, who coordinated Mason's ward three campaign, that produced Mason's lead over Sizemore.

Shackleton said she originally had planned to endorse Frank Rich, who ran unsuccessfully for the Council in 1974, if he had decided to run. When he didn't, Shackleton said, she endorsed Mason.

"We worked very closely with Hilda on the campaign all the way through from the beginning because we (Democrats for Mason) felt that she was the best one running," Shackleton said.