Since you parents will not have enough to pay for the cost of a nursing home, that means they do not have a large estate and the house is probably the bulk of their property. If that is the case, and you do not expect them to go to a nursing home for a number of years, you still should consider the quitclaim. There would be no gift tax because of the lifetime exclusion from gift tax, see She can not give away the house and keep title in her own name. In fact, if she is planning on selling the house, then giving the four of you the money, she would be better off keeping the house till then. If she owns the house at the time of the sale, there would be no income tax on the gain on the sale because it would have been her main residence for at least 2 of the last 5 years before the sale.
So the easiest way to do it is to have her keep the house. When she sells it, then give you four the money. Her lifetime exemption for the estate and gift tax would be applied and there would be no gift tax on the gifts. For an explanation of how this works, see
https://law.freeadvice.com/tax_law/gift_tax_law/unified_estate_gift_tax.htm.
However, be careful! There are very strict laws, with criminal penalties, designed to prevent people from giving their property away at the last moment, or even within a few years of the time that they enter a nursing home, if the result is that the Government will be expected to pay the costs of nursing home or other care, rather than the person himself from his or her assets.
The safest thing would be to engage an elder care attorney to help you create a plan that will both protect the assets and make them eligible for Government benefits.