Hi Anna, I'm sorry to be posting so late - I just spent two days helping my friend whose husband is terminal. In any case, you've gotten so much great advice and support here. I'm going to add some general thoughts since other people are interested, but if you want specific input, pm me and I'll give that privately.
First, you are not alone or at fault for your feelings in any way. You are in an extremely hard position. I don't know your history or his financial situation (and you don't have to tell me, of course!), so I'm going to be general. I see a lot of folks who feel resentful taking care of a parent, and more so if the parent was not always there for them. Only children have it even harder. Often the parent is losing capacity - which may or may not be happening in obvious ways - and that adds to the frustration. They are afraid to go out or do things on their own because they know something's wrong, but can't admit it openly. If that's the case, I'd suggest asking your dad's doctor to recommend a neuropsych eval to see if he's got some depression or impairment going on that can be addressed.
If, on the other hand, he's always been a PITA this way (or even if he does need additional help), you'll have to make some hard decisions about where you want to draw some boundaries.
Drop him off at the local senior center. If he hates that, tell him his options are limited unless he chips in somehow. You should not be in debt for his sake, and there are some programs that are set up to prevent that if he qualifies financially. An elder law attorney can really help with figuring that out, and you can find one through naela.org, the National Academy of Elder Law Attorneys.
Consider documenting his "debt" to you in writing - for one thing, that would be a way to get paid back if he ever does sell his house or need Medicaid and has to spend down his assets.
Talk to the elder law attorney about what resources are available in terms of respite if he qualifies financially. The Alzheimer's Association often provides such help to ALL elders on a sliding scale basis.
If you want to tell me more about his specific situation, I can give you better pointers - for instance, if he qualifies financially, you may be able to put him in a retirement home, some of which are really nice. Or if he has the resources (though it sounds like he doesn't), you can get a paid senior companion to play cards with him or take him to the movies.
Big hugs to you - this is more and more common, and there IS support out there if you can find the energy to pursue it.