While it is possible to book at the last minute, it is a better idea to book your car rental about 3 months in advance. There are two main reasons for this:
1- When you book early, you are sure to have the car you want on the dates you want. Some types of cars are virtually impossible to find at the last minute, such as minivans and SUVs.
2- The earlier you book, the more you save. It's like airline tickets: as you approach your travel dates and availability decreases, the laws of supply and demand dictate that the prices will go up!
These two reasons are especially valid if you are travelling in peak season.
Peak tourist seasons in the U.S. are:
1- July anf August
2- Mid-December to early January (holiday season)
3- April (school break)