NEW YORK -- On Sept. 17, New York's senators joined Mayor Edward I. Koch (D) in announcing the most ambitious voter registration drive ever attempted here, one that would use the senators' franking privilege to make mass mailings.

The effort to sign up some of New York City's 2 million unregistered voters was to be well under way by Thanksgiving, leaving plenty of time to boost the rolls for the state's April 19 presidential primary.

Three months later, however, the postage-paid registration forms have not gone out, and there is some concern that the effort may end too close to the Feb. 19 deadline for primary registration.

The setbacks involve the mundane mechanics of politics -- printing delays here and at the Senate print shop in Washington, and a lack of envelope-stuffing equipment.

"Maybe we underestimated the amount of time it would take," said Joel Copperman, Koch's director of operations. "It's a big job . . . 18 million pieces of paper stuffed into 3 million envelopes."

But Copperman said he was "ecstatic" that Sens. Daniel Patrick Moynihan (D) and Alfonse M. D'Amato (R) were using their congressional frank for the mailings, which he said should be ready next month.

"Practically speaking, it doesn't much matter if it goes out in January," he said. "Anybody who gets this package is either going to register in two or three days or throw it in the garbage."

The material has cleared the Senate panel that reviews mailings sent under the frank. A successful drive, in the view of some activists, could become a national model for enfranchising big-city voters who have never bothered to register.

"Part of the reason why urban needs have dropped off the national agenda is because cities are not only losing population to the suburbs, but also losing electoral clout," said Linda Davidoff, director of Human SERVE, a voter-registration advocacy group here.

Moynihan has an obvious stake in the outcome, as he is running for a third term next year. But some political observers have questioned why D'Amato, a Republican, would join a drive that is likely to recruit mainly unregistered Democrats. Insiders say D'Amato was enlisted by Koch, who heaped praise on the GOP senator during his reelection campaign last year.

"The electoral process works better when you have more people voting," D'Amato spokesman Ed Martin said. "This isn't a Republican or Democratic registration drive."

Locally, several city agencies and private firms have begun similar efforts.

The city's Human Resources Administration, for example, has mailed registration cards to client households and placed the cards at 243 welfare offices, shelters and other service centers. The City University of New York distributed forms during fall class registration and estimates that 25,000 students signed up. Con Edison sent cards to all new utility customers, about 223,000 to date.

On the other hand, the city's Housing Authority, citing printing delays, has not mailed any of the 220,000 cards it was supposed to send to public housing tenants, and Copperman said that mailing may be scrapped as duplicative.

All told, the city is spending $500,000 on the mailings, and New York state is kicking in $150,000 for printing.

Under the plan's centerpiece, Moynihan and D'Amato are to use their frank to send two postage-paid forms, in English and Spanish, to every city household. Individual members of Congress have made such mailings before, but not on this scale.

If the delays persist, the state's Board of Elections could have trouble coping with an influx of new registrants shortly before the February deadline, said Gene Russianoff of the New York Public Interest Research Group.

"The board did a terrible job in 1984," he said. "You'd sign up, show up on Election Day and boom, you wouldn't be able to vote. This has happened to me twice."

But Copperman said that while the elections board might be "swamped," it would have ample time to process the forms. He said the drive would be a "huge success" if it could recruit 500,000 voters.

U.S. voter registration consistently has ranked near the bottom of western democracies, and far behind the 95 percent sign-up rate in such countries as Canada. One-third of eligible Americans -- more than 46 million people -- are not registered to vote. In 1984, 38 percent of eligible New York City residents were not on the voting rolls.

Moreover, Brooklyn, Queens and the Bronx, along with several southern states, remain under Justice Department supervision as part of the Voting Rights Act.

Many states are trying to make it easier to register. Colorado allows voters to sign up with the same form they use to apply for a driver's license. Iowa and Minnesota passed laws this year requiring various state agencies to make registration forms available to the public.

Several states, including New Jersey, Pennsylvania, Texas and California, now provide postage-free registration forms, removing what Davidoff calls "a 22-cent poll tax." If the logistical kinks can be ironed out, New York hopes to join them.