I have always believed that according to the declaration of independence the government cannot sentence someone else to death. Because life is one of our unalienable rights granted by the Creator no one but the creator can take that right from anyone.
Interesting question. I am not sure what the constitutional standing of the Declaration of Independence is. Using that same logic, the government could never incarcerate anyone for any crime either since it also says we are endowed by our Creator with liberty.
I'm no lawyer, but I don't think the Declaration of Independence has any direct link to the Constitution.
Essentially, the DoI was a letter that said, "Dear British Empire -- We're no longer ruled by you. Here's why [lots of flowery language]. Not-So-Respectfully, The Rebels"
I'm sure Tidewater can quote more precise statistics, but as I remember, the colonial population was split into three roughly equal segments. About a third wanted independence, about a third wanted to stay in the Empire, and about a third didn't care one way or the other. So at the time it was written, the DoI had active backing from a distinct minority of the population.
A pretty audacious statement, when you think about it: a definite minority presuming to speak for the whole of the American colonies, up to and including inviting an armed response from the Brits, which they knew full well would ensue.
Whereas the Constitution was ratified by all the states, and therefore had the backing of a far bigger portion of the population.
The Constitution might incorporate some of the same overarching ideas and principles, but it's the foundation of our legal system. The DoI was just that -- telling the British Empire that we're going our own way. Two separate sets of purposes and implications.