BROOKLYN - The deadline to register to vote in New York City is Oct. 10, and on Sunday, high school seniors who are eligible to vote received a lot of attention.

Councilman Eric Gioia estimates that 7,000 high school seniors in New York City are eligible to vote, but haven?t registered.

This week, principals in all city high schools are being asked to remind students over 18 to register by filling out registration cards at school, printing an application from the Board of Elections Web site, visiting a local Board of Elections office or calling to have the form mailed directly.

Voter advocates believe the young demographic could be a force at the polls in this year?s presidential election.

?I've seen something I haven?t seen before and that's enthusiasm,? says Barbara Barr, of the League of Women Voters. ?If these young people get a chance to register, they will vote.?

The Board of Elections will host voter-registration drives in several dozen schools Oct. 7 from 12 p.m. to 9 p.m.