Perhaps the people who drafted the US Constitution would have had a chance to read Smith by 1787, but I can't imagine they would have really had a chance to fully digest and internalize the ideas being presented. They were almost certainly working from a firmly mercantilist mindset.
"Hutcheson had abandoned the psychological view of moral philosophy, claiming that motives were too fickle to be used as a basis for a philosophical system. Instead, he hypothesised a dedicated "sixth sense" to explain morality. This idea, to be taken up by David Hume (see Hume's A Treatise of Human Nature), claimed that man is pleased by utility. "
I think this is one of the first places to move away from a labor theory of value to a utility theory of value. I'm a dummy though so who knows.
Edit: Publication on or before 12 April 1759 should have had plenty of time to be read and discussed before the Contract Clause?*
^https://en.wikipedia.org/wiki/The_Theory_of_Moral_Sentiments