Thanks for all the feedback!
My main concern is this: if my father passes first, my mother will only have a very small social security pension (and the house). If she eventually needs to go into a nursing home, correct me if I'm wrong, but Medicaid will then take her assets, and 'look back' 5 years to recover anything transferred away.
My parents recently went through a lot to keep the house, and now they tell me they absolutely want me to get it, so I think I should take steps to protect it. I don't mind having it in my name, but I told them about my concern. They talked to a lawyer, however I think they just went with the simplest choice - doing an immediate transfer (with an umbrella policy for protection).
I was hoping someone here had gone through the same thing. It hasn't been signed over yet, so I'm asking BiggerPockets, and I greatly appreciate all your input. It looks like it'll be a good idea to contact a lawyer in my area that specializes in elder care, and then I'll post a follow-up. Thank you all again!