My mother may need to go into a nursing home soon. With Power of Attorney, can she transfer any of her assets to me just in case?

There is a five year "look back" for Medicaid, the program that pays for people unable to pay for their own care. She can't transfer her assets to you now and expect to go on Medicaid. She can give them to you, but (or you) will have to pay for up to five years or until her money runs out. You should see an estate or elder law attorney if you are considering any asset changes.
Carol

A parent can transfer assets to a child (regardless of the child's age) is if the child is receiving Social Security Disability.

I also highly recommend seeing an elder care attorney.