This may surprise some folks. It's well known that Washington, Adams, and Madison issued Thanksgiving proclamations (to a generic God), while Jefferson refused. And Madison, in his Detached Memoranda seemed to indicate it's improper for the federal government to do this (thus giving support to the notion that Founding-era practice is not dispositive, that indeed, it's entirely possible to raise a constitutional ideal one minute, then break it the next).
Before seeing this quotation in James H. Hutson's fine book, I didn't know that Adams too regretted issuing the Thanksgiving Proclamation. His words are quite interesting:
The National Fast, recommended by me turned me out of office. It was connected with the general assembly of the Presbyterian Church, which I had no concern in. That assembly has allarmed and alienated Quakers, Anabaptists, Mennonists, Moravians, Swedenborgians, Methodists, Catholicks, protestant Episcopalians, Arians, Socinians, Armenians, & & &, Atheists and Deists might be added. A general Suspicon prevailed that the Presbyterian Church was ambitious and aimed at an Establishment of a National Church. I was represented as a Presbyterian and at the head of this political and ecclesiastical Project. The secret whisper ran through them "Let us have Jefferson, Madison, Burr, any body, whether they be Philosophers, Deists, or even Atheists, rather than a Presbyterian President." This principle is at the bottom of the unpopularity of national Fasts and Thanksgivings. Nothing is more dreaded than the National Government meddling with Religion.
John Adams to Benjamin Rush, June 12, 1812. Old Family Letters, 392-93; taken from Hutson's The Founders on Religion, 101-02.