Although the Constitution does not specifically state that everyone has the right to free insurance, the very first paragraph has an entry that certainly could apply to the insurance scenario and the well being of Americans -
"Promote the General Welfare."
I would submit that one of the most important aspects of American life, or any life for that matter, is a person's health. The Constitution certainly could be looked at in this light when talking about Promoting the General Welfare - the very document establishing our country is concerned with the general welfare of its citizens - and certainly could be concerned with all having good health... to the point of promoting it as an important factor in the lives - generally - of all citizens. Certainly there are things the government doesn't specifically address that comes under this line, and many others. It's a working document, meant to be followed, difficult to change, but changeable, to be sure. And I think this line is food for thought when it comes to the issue. The Constitution is not meant to be rigidly looked at word for word in all situations, but held up as a standard for the good of the country, and there are certainly different ways to analyze it, learn from it, and perhaps even change public policy by looking at it differently, or as a guideline, depending on how you look at it.
Many people certainly subscribe to "providing for the common defense" as the entry right before it - and that one certainly has room for discussion, doesn't it?