Rental car prices and availability will vary dramatically based on demand. If demand is high for a specific period, then as you get closer to that time the prices will go up (sometimes significantly!), and individual locations may sell out. If demand is low, prices may drop as you get closer to the date.
Generally the best option for someone in your situation is to make a booking that allows you to cancel without a fee, and then keep an eye on prices as you get nearer to the time. If the prices drop, you can cancel your existing booking and make a new one. If it turns out you don't need the car, you can cancel the booking without a fee.
Given you are not from the US, if you end up making a booking whilst you are physically in the US you should make sure that your residency is correctly selected on the site you're booking from. If you don't do this, then the required insurances will not be included in your booking, and you will need to pay them at pickup which will increase the price significantly.