Do you believe in the right to life?
The right to life is not the same as the right to live.
The right to life means that nobody can actively take your life from you.
The right to live (which is what you seem to be proposing with the "right to health care") would necessarily carry with it a concomitant obligation upon everyone else to do all within their power to keep you alive.
So are you advocating for a "right to live"? Is society then under an obligation to keep you alive even as death is knocking on your door? If there is a "right to live" then the government would have a moral and legal obligation to provide not only for everyone's health insurance, but to actively provide everyone's medical treatment.
If there is a "right to health care" then the government would be obligated to ensure that everyone not only have access to it, but that everyone have it. In that case Obamacare certainly does not go far enough.