Christ never supported the government doing anything. He came to establish a heavenly kingdom not to support an earthly one. he did say we should be good citizens but nothing more than that.
and a heavenly kingdom is one of fruitful individual labor, not one of dependence. why should those who labor and enjoy the fruits of their labor have to bear the burden of providing healthcare to those who are unemployed, whether by choice or by circumstance.
Peter (or was that Somebody else called the Holy Spirit) said that those who do not work should not eat, which is a lot harsher, and more fundamental, than simply paying for the healthcare of others.
now, what are you gonna do about that ?