It's hard to see how 'life, liberty, and the pursuit of happiness' is antithetical to the concept of universal healthcare. And then there's the well-known preamble to the Constitution:

'We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, [...], promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution...'

Sure sounds like universal healthcare to me.