Before I go too far into this, I'm an Agnostic and I'm not here to try to convince Atheists to become Agnostic. Or believers into becoming Agnostic either. Religion is for people who want it or not. Not for people to try to force their beliefs on others and that goes for Agnostics, Atheists or believers. So no I don't believe our Constitutional Rights come from God, even if one exists, again I don't know if there's a God, (in case you're wondering why I'm Agnostic) which is why I don't believe or disbelieve, but a reason why I don't believe God gave us our rights, is because God wouldn't be qualified to give us our rights.
God is not qualified to give us our rights because if he did, they wouldn't be as great as they are now. They would either be less of them, which of course would be bad. Because that would mean there would be more power for government. Not a good thing and of course government would say that, "well we have this power to use on your behalf". Well my response would be, how come I can't use the power that you just took away from me, for myself. I would love to hear the answer to that. An example of having too many rights would be the right to take innocent people's freedom away from them, like the right to kill or hurt people intentionally, or unintentionally.
Another reason why God wouldn't be qualified to give us our rights, because if he's so great, why are there so many horrible things in the World. Why so many people starving, why do we have bigotry, we do we have so much poverty, why do we have so much ignorance, in the United States and around the World, how the hell does Rick Santorum and Michelle Bachmann ever become qualified to run for President of the United States.
Why do have so many disasters, why do we have so many people living under authoritarian rule, especially East of Europe but also in the Slavic States and so forth. If God was so great, there wouldn't be so many horrible things going on in the world. We wouldn't of had to go through slavery in America, we would've never of had African Slaves or any other slaves, the Jewish Holocaust would've never of happened and so forth. So God didn't give us our rights, because the people who wrote the U.S. Bill of Rights knew better.