No. Social contract speaks to the general welfare. Rich and poor alike benefit equally from sewer systems, street lights, shared roads, and police and fire protection. Opportunities for all are enhanced by a community being made more attractive by the presence of these things, and therefore more commerce and industry will settle in that community and benefit all. It is not assumed that the rich will pay so that the poor don't have to, or that some citizens are worthy to receive the benefits, but not all. Nor is anybody who chooses to opt out penalized. Those who choose to live in the community accept the social contract. Those who wish to live outside the community are free to do so complete with their own well, own septic system, own private road, own utility system etc. There are a number of areas of New Mexico in which all citizens are doing just that.
That is social contract.
A nationalized healthcare system requires the rich to pay for the poor, does not allow anybody to opt out of it and do their own thing, penalizes those who don't want to participate, and takes away freedom from people, and dictates what healthcare the people will receive.
That is socialism.