Yet further googles turned up this link with a great explanation.
The original discussion came from Theodore Dwight Weld's 1839 book: American Slavery As It Is: Testimony of a Thousand Witnesses.
Weld wrote:
But Weld and all other historians commenting on this question end up punting and straddling both sides.
Leonard Richards (Slave Power) put it this way:
"Whatever Randolph had in mind, his words stuck."
The key point is that "Doughface" was a derogatory term, used by Southerners to insult Northerners who were trying to please them by giving into Southern demands.
Of course, in my context on this thread, I mean nothing of the sort.
Instead, I mean Northerners who share the South's commitment to true conservative principles.
So I'm not trying to insult anyone, but perhaps to rehabilitate the term "Doughface" in a modern, positive sense.
Maybe it's the other way around. Instead of a Wallace or a Thurmond, someone with deep Southern roots, Southern states are going for guys from Pennsylvania (though both have Southern ties).
Newt Gingrich or Rick Santorum as a spokesman for "Southern conservative principles" may be an indication of how much things have changed in fifty years or so. Of course, the fact that these guys are a lot less likely to carry states like Pennsylvania does tend to cloud things.