As therefore the creator is a being, not only of infinite power, and wisdom, but also of infinite goodness, he has been pleased so to contrive the constitution and frame of humanity, that we should want no other prompter to inquire after and pursue the rule of right, but only our own self-love, that universal principle of action. For he has so intimately connected, so inseparably interwoven the laws of eternal justice with the happiness of each individual, that the latter cannot be attained but by observing the former; and, if the former be punctually obeyed, it cannot but induce the latter. In consequence of which mutual connection of justice and human felicity, he has not perplexed the law of nature with a multitude of abstracted rules and precepts, referring merely to the fitness or unfitness of things, as some have vainly surmised; but has graciously reduced the rule of obedience to this one paternal precept, "that man should pursue his own true and substantial happiness." This is the foundation of what we call ethics, or natural law.
Sir William Blackstone, Commentaries on the Laws of England, Book I, Part I, Section II.
Natural law theories can diverge from each other in a number of ways, and one of them is what they take to be the fundamental precept. Aquinas, of course, because he takes the fundamental precept to be to reasoning about obligation what the principle of noncontradiction is to theoretical reasoning, holds that it is "Good is to be done and sought, bad to be avoided" when it is applied to the common good of the human race. Suarez follows him in this, although I'm inclined to think he has a narrower understanding of it -- he qualifies it by saying that good should be understood as honestas and the bad as turpitude, which is maybe a way of saying with Aquinas that we get the precept when we apply the principle to common good in particular, but I'm not really sure. Scotus, if I don't misunderstand him, takes the first precept to be "God (as infinite good) is to be loved". Blackstone's "Man should pursue his own true and substantial happiness" is a very different one. It need not be said that all parties would in fact agree with all of these as truths; Aquinas holds that God should be loved, and Scotus that good is to be done and sought, and both that our true and substantial happiness is to be pursued. But recognizing these as true and recognizing them as law are different things (as Aquinas makes quite clear), and you get a rather different view depending on which of these you take as the root precept.
Reading this passage in context, it seems undeniable that Jefferson's use in the Declaration of Independence is ultimately from Blackstone. Jefferson himself does not seem to have liked Blackstone very much at all, but there are too many similarities to be accidental. It's sometimes said to have been an indirect influence; Jefferson is thought to have been influenced by the Virginia Declaration of Rights, which was written up by George Mason. This influence is pretty obvious if you look at the first article of the Virginia Declaration. But I'm not sure this completely closes the lid; there are other echoes in the Declaration suggestive of Blackstone, so maybe it's not all through Mason. I don't know.
ADDED LATER: I should have also remarked on Blackstone's rejection of moral rationalism -- the "abstracted rules and precepts, referring merely to the fitness or unfitness of things". This is an approach to ethics that begins with Malebranche; Hume, complaining about it in the footnote for Enquiry Concerning the Principles of Morals, Section III, Part II, calls it an "abstract theory of morals".