The U.S. Declaration of Independence is a magnificent inspirational document. I read it to my kids every Fourth of July, whether they want to hear it or not. But I don't think it offers much help in interpreting the Constitution.
True, it is a document of the founding era, written and adopted by educated people of the same background, education and outlook as the people who wrote the Constitution (indeed many of the very same people). So the way it uses language may be relevant to the way the Constitution uses language, to the extent the language they use overlaps. But in this sense it is no different from and no more significant for constitutional interpretation than other documents of the founding era written by educated people of the same background, education and outlook as the people who wrote the Constitution. And in fact the language of the Declaration and the Constitution does not overlap very much, at least not in useful ways.
Some people would give the Declaration greater weight, as a reflection of values that inspired the Constitution, and thus of values that we should read into the Constitution even if they are not expressly there in the Constitution's text. But I am skeptical. The two documents are very different. The Declaration is fundamentally a rhetorical document, meant to persuade the world — and more immediately and significantly, to persuade wavering Americans — that the revolutionaries' cause was just. The Constitution is fundamentally a legal document, meant to spell out a form of government to which Americans would be bound, and by which that government would be bound. Perhaps the Constitution implemented the rhetorical ideals of the Declaration, but perhaps it didn't (and perhaps it was the worse for that). The way to see if the Constitution implemented the ideals of the Declaration is to look at the Constitution's text, not to assume that it did.
When I hear people appeal to the ideals of the Declaration in interpreting the Constitution, I suspect that they are trying to find something in the Constitution that isn't there, and so must be found by other means than reading the text. Of course, if they are using the ideals of the Declaration to reinforce what's in the Constitution's text, that's fine — but also isn't adding all that much.
ADDED: A possibly dissenting view from Randy Barnett: What the Declaration of Independence Really Claimed (though I don't disagree with anything he says in the post).
Posted at 6:50 AM