What would the founders do?

Steve Waldman has a good overview of the declining inclusivity of inaugural prayers over the past half-century. I find his overall argument persuasive and would only take slight exception to his claim that the country's founders would have disagreed on the desirability of having prayers at the inauguration at all. Steve bases his claim on the differing views of Washington, Adams, and Madison on presidential prayer proclamations. But it's worth noting that none of the above, nor any other president for nearly a century (until Chester Arthur, who took office in 1881) so much as used the phrase "so help me God" when taking the oath of office. This was to be a secular ritual, not a sacred rite complete with invocation and benediction. Yes, most pre-invocation presidents employed a Bible, but that ought to be seen in the usual common law sense of oath-taking in a courtroom. So while I have no particular enthusiasm for Newdow et al.'s efforts to get the prayers out of the Inauguration, I do think there would have been a consensus among that first generation of national leaders to keep religion out of it--lest, as Madison said of the proclamations, it imply and nourish "the erroneous idea of a national religion."