I think that it's going to be almost impossible to find a car rental that cheap... especially in Florida at that time of year.
The most important things to do to get the best car rental rate possible is compare multiple companies, compare totals and not just the base rate per day, and book as far in advance as you can.
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The first thing you can do is check a booking site so that I could compare multiple auto rental companies at once. You can use any site to do this, like Kayak.com, Orbitz.com, Hotwire.com, etc. This way you can compare base rates quickly to see if a rental car for under 20 dollars per day is an option.
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Tips on Finding Last Minute Specials
You can try going to different car rental websites and checking prices using promo codes for seniors or other programs that you might belong to. There are hundreds of membership programs and professional associations that offer discount codes to their members.
The only other option to try and find a rental car for under 20 dollars per day, that I can suggest, is that you try going to Priceline.com and bidding for a price -- But be very careful and make sure that you know all the conditions for this type of booking:
On priceline.com just scroll down to where you see "Name Your Own Price" and pick rental cars.
After plugging in your dates and times, click bid now.
You can list a price per day to bid...just keep in mind that the taxes and fees charged by the rental company are extra and are not included in the per day bid that you make. Even if you bid and are accepted for a rental car for under 20 dollars per day, keep in mind that there will be taxes and fees added that will bring the price of the reservation up to more than $20 per day.
You will be asked to fill out a reservation form and give your credit card number.
Although you may be able to get a cheaper price this way, than directly from the car rental company, it's very, very important to know that this kind of booking is extremely inflexible. You may find that the restrictions and terms and conditions may not be worth the savings.
Please keep in mind:
Priceline cars are usually non-refundable, non-transferable and non-changeable even if the reservation is not used. You cannot change the reservation to another date or time or cancel it -- once it's accepted you are charged, whether or not you ever pick it up -- even if due to illness, weather or cancelled or delayed flights. (This is where you may find that the restrictions and terms may not be worth the savings... if you book directly through the rental company, you can cancel your reservation at any time and will not be required to give your credit card up front).
If your offer is accepted, the reservation is locked in and charged to your credit card. If your offer is not accepted, your credit card will not be charged.
You will not know which provider you will have a reservation with, unless your bid is accepted and until after your credit card is charged.
I hope this helps and good luck with your reservations; I hope you find a rental car for under 20 dollars per day somewhere!