That's not how the car rental biz works. When they have an abundance of cars the price goes down. The prices change daily and I have seen them change hourly.
HotWire and others, allow you to see multiple companies at the same time. Plug in single dates and see what happens. Try tomorrow, and then try the next day. Try Saturday or Sunday. Often one day rental can be nearly the same as a week. Play around until you get a feel for what you want,
With HotWire, you have to pay upfront. Sometimes I will get a price from a site like HotWire, then go to the individual car rental site and find they match the price. Car rental company reservations do not require payment upfront.