The North and South Terminals are shut down between roughly midnight and 5am. So you would not be able to "overnight" there.

The main terminal is probably open 24 hours, but most of the seating is not configured for sleeping (armrests).

Your best bet is to just Priceline an airport area hotel or take a taxi. You can also do an airport shuttle, but they like to show up like three hours before departure. Both the taxi and the shuttle will probably be more then Pricelining an airport hotel.