The odds will always be against you; however, they will be a bit less if you travel on a non Holiday and between Sunday night and Thursday night.
During our 46 round trip drives from NJ to WDW, we nearly always made a reservation in advance, based upon the place we expected to get to if we were doing an overnight stay (we also did over a dozen straight-thru drives), like Pooler, GA; or Yulee, Palm Coast, or Deltona, FL. And we made these reservations on the road, usually before 6 p.m. There is no worse feeling than driving to hotels and asking for a reservation that doesn't exist. We experienced that on our first drive in 2002.
Note #1: we have made multiple reservations in the past, cancelling the other(s) based upon whether we could reach a certain Holiday Inn by a certain time. Check with each hotel if your decide to try that since all hotels have different refund policies based upon different times.
Note #2: Staying at Yulee, for example, will give you a three-hour drive to WDW.
Good luck.
All the best!