I had a few occasions in which I made a reservation same day without any issues. If my memory serves me correctly, rate was the same. I actually just input a rental request for tomorrow and the rate was no different.
Free rental days work for anything. I made reservations for a luxury car at SFO in a few months with my free credits. I had previously used one on a reservation I made same day as well. ^
My company recently forced me to move to Hertz... I miss National already.
cheers.