I've done this before, in Sep 2013, flying from EWR to YYZ. My flight was at 6 am, so I took the njtransit train to the airport at around 11 pm or so, on a sunday night, for a monday morning flight. Went in, and pretty sure I went through security too, as I hung out near the duty free shop. Now, this was (technically) an international flight, but I wouldn't think it would make a difference. There were some tables I was able to stretch out and and get a little shut eye.

Some others were doing the same, but not many really, I don't think you would have a problem though.

Good Luck!