Katie, "Common Sense" was published in 1776. It is my belief that both documents could have influenced the writers of the declaration. Jefferson said it most eloquently, and I see no reason to think otherwise.

"[n]ot to find out new principles or new arguments, never before thought of, not merely to say things which had never been said before; but to place before mankind the common sense of the subject, in terms so plain and firm as to command their assent, and to justify ourselves in the independent stand we are compelled to take. Neither aiming at originality of principle or sentiment, nor yet copied from any particular and previous writing, it was intended to be an expression of the American mind, and to give to that expression the proper tone and spirit called for by the occasion."(history.com)