If I die, who will care for my spouse?

BoxBoy11: Imho, seek out an elder law attorney.

See lawyer that specializes in elder care and your banker. Every state has different rules regarding this situation. They can let you know which legal documents and banking accounts would be best for your situation. Generally, if nobody can care for your spouse, she becomes a ward of the state and a legal guardian will be appointed by the courts. Any assets she has will be used for her care. If she runs out of assets, then her guardian will file for Medicaid for her.

This is a concern that most if not all caregivers have.
I saw an Elder Care Attorney (was seeing one anyway due to the Guardianship I had to have..long story) I had a Will done for myself with a Special Needs Trust that would provide for him if something happened to me.
A set up like that would care for her in the event of your death or if you became incapacitated. You should have a POA, someone to act on your behalf if it came to that. You can appoint a friend, relative or the lawyer can handle that.
If there is nothing like that set up and there are no relatives she would become a Ward of the State and any monies from your estate would be used for her care with the State having control over the money and where she is placed. (the state could move her to another facility if they chose to.)

You should see an Elder Law Attorney. This person can suggest a licensed Financial Fiduciary to take over managing the estate that is left. You will want to get a good recommend, a person licensed if that is required in your state, and you will periodically want to contact this person, updating them about your estate and your expectations on your death.

In the absence of suitable volunteers, your state will take over. An application for guardianship will be made and the court will appoint an official guardian to manage her care under the court's regular (if infrequent) supervision.

Take good care of yourself anyway, and don't let this possibility add to your stress levels. If she's already well looked after it's reasonable to expect that to continue - nothing appalling will happen to her.