I know that for the most the Confederates revered the founding fathers and the revolutionary generation, and accused the north of trampling on the founding principles, and even put George Washington on their national seal.

However, there are a few scattered anecdotes and bits of trivia that seem to suggest another strain of thought--one that spurned the American legacy outright.

For example,

There's a pretty well-known/popular song from after the war called "The Good 'Ol Rebel.". It's a lament of the southern defeat, but includes the following lyrics:

I hates the Constitution, this great republic, too...I hates the Declaration of Independence, too!

This strikes me as interesting because it seems to indicate a rejection not only of the contemporary (1865 contemporary, that is) federal government, but of even the earliest symbols of the American republic.

I get that the song is a little tongue in cheek, but it's still a long list of things associated with the "north" that a the author imagines a stereotypical 'reb' might hate, so it still seems telling to me that he throws in the Constitution and the Declaration.

Alexander Stephens' infamous Cornerstone Speech seems to recapitulate some of the same ideas in a more sophisticated fashion, particularly when he says:

Our new government is founded upon exactly the opposite [of Thomas Jefferson's] ideas

According to Don H. Doyle's, The Cause of All Nations:

South Carolina’s leading men seemed especially eager to let Russell know of their feelings of kinship with the European aristocracy, whose landed wealth and habits of mastery alone bred the proper requisites for public leadership. Russell was fascinated by their repeated expressions “of regret for the rebellion of 1776 and the desire that if it came to the worst England would receive back her erring children or give them a prince under whom they could secure a monarchical form of government.” (Louisianans, he later learned in his travels, preferred reunion with their former “mother country,” France.) There was general agreement that this desire for reunion with Britain could not be practically gratified, at least not until independence was secured, Russell told his readers, “but the admiration for monarchical institutions on the English model, for privileged classes, and for a landed aristocracy and gentry, is undisguised and apparently genuine.”

So how prevalent was the sentiment among Confederates that "this whole thing was a mistake--let's start over"? Was it common or almost negligible?