From Noah Feldman in Divided by God:

The framers are invoked on both sides of the debate about religious symbolism… [but] they were not especially concerned with public religious symbolism one way or the other. They were supremely untroubled by norms like the opening of legislative sessions with symbolic prayers.

This institutional experiment had little to say about religious symbolism. It was concerned with avoiding actual coercion and with disentangling church and state, which had been historically intertwined in the Christian West. So secularists do not really get the better of the argument about symbolism when they point out that the Constitution does not mention God or Jesus. The reason the Constitution does not mention Christianity is that the framers were creating government institutions that had no authority to pronounce on matters of religion, not because the framers themselves were secularists.

… They did not think that the state needed to be protected from the dangers of religious influence, nor were they particularly concerned with keeping religious symbolism out of the public sphere. For that matter, American religion, too, was very different than it is today. Church attendance was low, at least by today’s standards. There was no national movement devoted to promoting the role of religion in public life.