My mother is worried that someday she might have to go to a nursing home. She wants to place all of her six kids names on a Quit Claim deed in order to keep the nursing home from taking her house. I want to know if the grantees (her kids) would be charged a gift tax.

No, they would not be charged a gift tax, but you mom would be. If the amount that each child gets is over $12K, then there would be gift taxes involved.

What would be better is to sell the property taking a life estate to the offspring, She can then take a mortgage. She can then forgive $12K per year per child until the mortgage is paid off.