"Life" means food, clothing, shelter and safety (I put medical assistance in this last category). "The pursuit of happiness" can mean the right to be left alone, working to get a good education, the right to worship or not where you please, or it can mean buying everything your neighbors have. "The pursuit of happiness" can't be nailed down at all. "Life" has its hard cases, but is mostly straightforward. The general welfare is best served by making sure that the conditions of life are accessible to all the people, so they may then practice the ways of liberty and pursue happiness, however profoundly or trivially they see it, as well as they are able.
Your interpretation of this phrase depends on the current attempts to reconstruct the concept of rights into "positive" rights, i.e. the right to make another person support us if we need it. This is not what the founders intended. The Declaration phrase harks back to John Locke:
"Man, being born, as has been proved, with a title to perfect freedom and an uncontrolled enjoyment of all the rights and privileges of the Law of Nature, equally with any other man, or number of men in the world, hath by nature a power not only to preserve his property--that is, his life, liberty, and estate, against the injuries and attempts of other men."
But, suppose we accept your definition of "life" as it stands, and we accept the liberal thesis that government-provided medical care is the only proper way to provide medical care to all Americans. Then in what way can anyone logically object to the government providing everyone in America all of their food, clothing, and shelter? Where is the point where one says "stop here?"
And what happens when you run out of people to take that wealth from in the first place? History has a lot of examples.
There is a big difference between programs to help those who cannot help themselves, and the goal of placing the entire population (except the rich) on the Federal dole.
The latter is the goal of those pushing universal medical care, despite the fact that about 80 percent of people surveyed are just fine with their current medical plans.
This isn't about compassion, it's about power, and until that's finally understood, this debate is going to go nowhere in Washington or elsewhere.
(Just as an unrelated aside, you might want to look at the history of Texas, which is a bit more complex. As I recall, Crockett was fighting the Spanish Mexicans, who didn't exactly buy the territory with cash from the natives.)
"As a matter of fact and law, the governing rights of the States are all of those which have not been surrendered to the National Government by the Constitution or its amendments. Wisely or unwisely, people know that under the Eighteenth Amendment Congress has been given the right to legislate on this particular subject, but this is not the case in the matter of a great number of other vital problems of government, such as the conduct of public utilities, of banks, of insurance, of business, of agriculture, of education, of social welfare and of a dozen other important features. In these, Washington must not be encouraged to interfere." -- Franklin Delano Roosevelt, on Prohibition, in 1930
