I've talked to the Budget/Avis at the FBO before and they have told me they wait for all delayed flights (and in this case a late flight). As far as the Enterprise/National counter in the terminal, its part of their lease that they must remain open until airport operations are done for the day even in the case of a delayed flight.

(It says 6am to 11pm but this was prior to the extended flight schedule but covers that by saying that they will extend their hours till airline operations cease for the day)

http://nj.gov/counties/mercer/procur...rt%20lease.pdf
Page 8
"The Vendors shall be required to make uniformed, professionally trained
personnel available at the Airport Terminal Building during normal operational
hours (6:00 A.M. to 11:00 P.M.) or in the event of delayed flights, any other
emergency or request of the Airport Manager, the Vendor will
extend their hours beyond the normal operating hours until airline operations cease for the day"

Enterprise/National: (609) 882-4132
Avis/Budget: (609) 434-1791

Try quoting both of them because I've found that Avis Budget is cheaper (probably due to their location in the FBO).