If you have a coffee maker in your room you really won't need it. Just bring a little bit of *white* vinegar with you in one of those little travel bottles that you buy for shampoo. When you first arrive at your hotel, run a pot of water with about a tablespoon of vinegar in it through the coffeemaker's cycle; that should flush out the coffee taste. Run a second water-only pot after that to thoroughly clear out the vinegar, and then from there out you can use the hot water from the coffeepot to make tea. It is very quick. We have LOTS of tea-drinkers in my family; this always works like a charm for them. They just make it a practice to always carry a little bottle of white vinegar in their toiletries bag.
BTW, Orlando tap water is heavily chlorinated and does not taste especially good. If you have a car or grocery stop, you might want to get a gallon jug of distilled water to use for making tea.
Of course, if you have a coffee-drinker in the family who will be using the coffeemaker, then it's back to the kettle plan. If will not cause security issues if it is in your checked baggage.