AFAIK, there are two that are $10, but you're right, pickings are slim at that price. $20 is more accurate, and on these phones that will not include airtime, that will normally be an add'l $20 card for the time that you will be using it.
Tracfone (
www.tracfone.com) has phones priced in this range, but their service does not include a web browsing option, and you may or may not have texting available. The per-minute charge on this one is cheapest.
Virgin Mobile (
www.virginmobileusa.com) also does, and their Paylo Basic plan (their very cheapest) will cost you $20 to activate for 90 days on top of the cost of the phone: that will get you talk, texting and browsing, all of which deduct time from the phone account. Their only $10 phone is the Samsung 340 (formerly called the Mantra), which is a great little phone with a good battery; we have two of them in our house. Unfortunately, the website is sold out of them at the moment.
The problem with the really cheap PAYG phone in the US right now is that those plans are being phased out in favor of unlimited monthly access rates, which are nice if you are using the phone often. However, because the companies make the most money off the fancier smartphones w/ those unlimited plans, they have been dropping the cheapest basic phones.
The simplest place to buy these phones in Orlando would be Target; there is one on Orange Blossom Trail en route from the airport to WDW, off the Greenway (South Exit 417).
Walmart normally doesn't carry that many national brand prepaids any longer because they are now selling their own brand, called Straight Talk (which isn't really priced attractively to someone with your needs, it assumes a longer-term commitment and gives the best rates for buying time in quantity.)
If your CC will work on a US website, the easiest way for you to get the phone is to order it online (w/ airtime) a week or so before you come, and have it shipped directly to your resort to be held for your arrival. You can activate the accounts by calling on your room phone.