You can plant grass seed as late as October 25 in the Northeast. The grass will grow a small amount, turn dormant, and then resume growing in the spring. Plant in the southern part of the state up until October 1.
Fescue grass seed grows well when planted in late fall. Sow it between late August and mid-October.
It is possible to plant grass seed even later in the year than October. It's a process called dormant seeding. The seed stays dormant until the spring warm-up. The process is unreliable, however, and should only be attempted if there will be snow cover on top of the seeds right after they are dispersed.