Socialism is State control of the means of production and determining which products will be produced and how those products will be distributed.  A public health insurance company (like Medicare and Medicaid) is no more socialist than education, the military, postal services, and public safety.

Conservatives love to claim that anytime the government gets involved it is socialism.  But, socialism actually involves absolute control over resources.  Just because the government creates an enterprise that will compete with private enterprise, it does not automatically follow that all private enterprise will be forced out of that industry.  There are private carriers, educational institutions, medical insurers and pension providers. 

The red menace is nothing more than a scare tactic that conservatives like to throw out to convince the ignorant that any government involvement is nothing more than socialist.  If socialism is so evil, why are these conservatives not fighting to actually scale back "socialist" programs?  Because they know they are full of it when they make such claims.