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They assumed, wrongly, that this nation by default would be a Christian nation because the separate and sovereign states would do their duty.

OK, so since they didn't mention God or religion, you're saying they didn't bother because it was so obvious it wasn't necessary?
I have a feeling that no matter what the Federal Constitution said, with the possible exception of "All must worship Satan" you'd be able to spin it into them really meaning to establish the US as a Christian nation even though they didn't actually say it.

No what I'm saying is consider the time the Constitution was written. According to several historians, 53 of the 55 signers of the document attended church regularly or called themselves Christian in the sense of the word at the time. The federal government was designed to be quite weak. It had specific powers and would not be involved in most state decisions. There would be no need to state the federal government was Christian and if it were in the Constitution, the dangers of a federal denomination could be realized.

It is clear from the statements listed above the states recognized Almighty God and by Madison's own statement in #45, reiterated in the 10th Amendment, they were free to establish state denominations. And they were free not to. It was a choice left to the states. Under the Constitution, the US was never established as a Christian nation, however from the statements above it is clear the separate and sovereign states recognized 'Almighty God' (a clear reference to the Judeo-Christian God) as the source for their rights and derived powers. These were the states whose legislatures would elect Senators and the President. One could easily assume, rightly so, that the men sent to the capitol would be Christian and make their decisions accordingly.