I have been involved in a number of arguments in which I contend one can not be an atheist, and a committed American patriot. Certainly there are atheists who have fought and died for this nation, and who love this nation dearly for the freedom it has given them to live as atheists. Having conceded all of that, they fail to acknowledge a power greater than humanity with the authority to grant inalienable rights.
John Adams would agree with you:
"Our Constitution was made only for a moral and religious people. It is wholly inadequate to the government of any other." - John Adams