I hear considerable derision around town, even laughter, about the long-shot chances of mayoral hopeful Carol Schwartz. In this 70 percent black city where Democrats outnumber Republicans 10 to 1, people say, a well-to-do, white Republican from the District's richest ward has about as much chance of beating Marion Barry as a snowball in the lower reaches.

But despite the recent Washington Post poll that showed Barry leading Schwartz more than 5 to 2, local Democratic voters may find that the laugh is on them in November if Schwartz's candidacy is taken too lightly.

A former member of the D.C. school board, Schwartz, 42, won an at-large seat on the City Council 18 months ago, prevailing against the heavily backed incumbent, the Rev. Jerry Moore Jr. Unpopular with many of her fellow council members, Schwartz is criticized by some as not having mastered her present job and one who overestimates herself thinking she can handle the city's highest elected office.

"She would be well advised to spend more time learning her job and how the council operates," grumbled veteran Polly Shackleton (D-Ward 3) after Schwartz's announcement. Defending herself, Schwartz complains that the council's seniority system has blocked her from effectively exercising power.

But Schwartz's candidacy takes on added meaning for reasons that have more to do with circumstances than with Schwartz herself.

In the two previous mayoral campaigns since home rule, the heaviest vote has taken place in the September Democratic primary. With Schwartz's entry into the race and only several lesser-known Democrats opposing Barry, the traditional pattern will change and the most important race will take place not in September but on Nov. 4. Therefore, if District residents hold to their traditional voting patterns, the smaller November turnout could work in Schwartz's favor.

District residents cast 122,526 votes in the 1982 November election, according to the D.C. Board of Elections. Of that number, Barry received 93,364 votes, 2 percent of the ballots were disqualified and four opponents split the remaining votes.

If 100,000 voters went to the polls, however, and if the city's 30,000 Republicans vote for Schwartz along with 15,000 Democrats, it could be a close election. If enough Democrats stay home, Schwartz could win. After all, she drew 53,782 votes in the general election 18 months ago, from predominantly white Ward 3 and the mixed populations of wards 1,2 and 6.

Of course, if voters turn out in larger numbers than usual in November, it could help Barry, who not only will have to campaign vigorously until November for the first time but also must maintain momentum amid considerable voter apathy.

But momentum is not Barry's only problem. Residents are revising their opinion of Barry's job performance, with those expressing disapproval increasing by almost half, according to the Post poll. So Barry could well encounter a Democratic voter backlash of discontent.

In addition to the "Anybody but Barry" critics, there are those who are frustrated by Barry's handling of such issues as prison overcrowding and by repeated charges of wrongdoing in his administration. They may vote for someone else.

Those who generally like Barry's programs but who resent being taken for granted and his "mayor for life" attitude may want to send him a message by staying home. Finally, there are those who, while believing that Barry is an honest man, object to how his administration has tarnished the city's image.

Schwartz has made it clear that she intends to exploit every iota of discontent she can find. When she announced for mayor in late June, she came out swinging: "I am running because I cannot accept an administration which spends millions of dollars on 'consultant contracts' for cronies but cannot find the money to answer the police emergency phone lines."

None of this is to say that the wily, hard-working political pro who inhabits the District Building has to worry seriously about finding a new job after Nov. 4, since he is way out in front of everybody. But this campaign is likely to be important for the future of the city for both the messages the candidates send to the voters and the messages the voters send back. Either way, the bottom line is clear: This fall is no time for District voters to sit back in apathy.