Medicare and social security are not entitlements as they are paid for during the life time of the recipient. It is a government run insurance program. Just like the private health insurance that you pay into - or your employer pays into for you.
What would you do in this scenario?
A young man is working, paying his taxes, raising his family and suddenly, he is suddenly severely disabled by disease or accident. If there is no social security or medicare, he can't get the medical help he needs; his income is gone so what does he do for food and shelter? Do we just shoot him so that he isn't a drag on society or do we keep funding social security and medicare so that he is taken care of and his children are able to eat, go to school and hopefully go onto college and become gainfully employed, paying taxes into the social security and medicare system.