It's no fun to point out that the Declaration of Independence has no legal force, so let me take a different tack.
The declaration's invocation of "unalienable rights" was not just filler, of course, it was fundamental to the Founder's political philosophy. I would argue that the Founders sought to embed the Declaration's recognition of natural rights into the Constitution first via the Privileges and Immunities clause of Article IV and then, when that wasn't explicit enough for anti-federalists, they proposed the ninth amendment protecting unenumerated rights "retained by the people.". In fact the entire Bill of Rights assumes a natural rights background, for it never purports to create rights, it simply protects those rights from federal interference.
Both the ninth amendment and "privileges and immunities" have become dead letters in our jurisprudence. Many conservatives are afraid to revive them, for fear of unleashing more judicial activism. But if we're originalists how can we let any part of the text languish? Especially ones so near and dear to the great Declaration?