No, and no. The founding fathers of America, DID trust in God. But if this is truly a country that has "freedom of/from religion", then there is nothing wrong with that.
But if I may offer my personal rant in a tangeant of the problem you pointed out, the simple fact is that this is America, so if we (Christians) want to "win it back" then it must be as Americans, not as Christians.
But who is saying America is God's Kingdom on Earth, it is "our" holy nation and trying to "Christianize" America?
Nobody. It's just non-Christians. And of course we think that non-Christians must not be American, because America is God's Kingdom, right?
Wrong because we worship the great pagan god America we believe in the American story that it has always understood itself as God's Kingdom on Earth, and so we think we should "win back America."
Can America be conquered by God's Kingdom? Sure, I imagine that that is possible. But why are so we busy trying to take control of America by America's means when we should be taking part in God's redemption of the world in the Church by God's means?
The "Christian" and American right movement in the Culture War (pushing their agenda to restore America to its "Christian roots") doesn't exactly make us look good to the world, of course, but as non-Christian Americans, I think.
When you commit the Church to being identified with an American history, it had better be right. (Say, for instance, "We inherited God's land" Of course, that's also basic theology.) The problem is that in this case the "Christian" and American agenda has no such hope.
What is the result? First of all, the Church looks very stupid. We're trying to play the world's game and we're just doing a worse job at it. If you want to be openly mocked, for good reason, have the arrogance to push the 'right movement.' Second, and more importantly, Christians are revealed for the arrogant bigots that we are. We don't like the fact that somebody else is "winning" the American ratrace, so we've got to fight back. And if the misled souls can do anything, they can smell a flimsy power play like this one. They know we're just trying to enlist the American government to aid us in our quest for power over our enemies. This may make people within the Church feel good about themselves, but it certainly won't tell the world that we are a people of the peace of Christ who are out for the good of the world.
What this tells the world is that we define ourselves
against "the other," and "the other" is them. We don't define ourselves by the Christ who is our Head. We don't define ourselves as the ones called out to serve the world. We define ourselves as the ones who are battling "The Democrats" "The Secularists" or "The Atheists" or whatever. But our battle is with the principalities and powers, not merely the Democrats or Secularists. Battles with the Democrats or Atheists are for people trying to participate in the American story,
not a Christian one.
So, mock away, atheists, and feel free to express your fear of Christians. We're crazy.