I've heard about the "constitution hanging by a thread" before, but not of the "official" (or unofficial) White Horse Prophecy until I read the article about it, and subsequent letters to the editor in the Tribune.
To find out more, I googled, and found an interesting article from the Wall Street Journal.
Here is a nice little excerpt...
"There have been several Republicans that I have known who thought that they were that individual," says Mr. Hartley [executive director of the Utah Republican Party], citing Todd Nielson, a GOP congressional candidate who failed in the 1996 state primary and Republican LaVar Christensen, currently vying for a seat for Utah's Second Congressional District. They have intimated to him that "the Constitution's hanging by a thread, and that they would be there to defend the Constitution," says Mr. Hartley.
...[but] frankly, I would worry about anybody who thought they were fulfilling prophecy".
I apologize for the (minor) change in context. It made the article more amusing.