Question, since you're obviously thinking this through. Would the argument along the line of Democrats only capable of nominating candidates of the caliber of a Carter or Clinton be effective in reminding voters of what happens when a Democrat is elected?
I wouldn't say I'm truly "thinking this through," as much as dredging up things I've picked up from others over the decades. As a 50 year old who happens to be a news junkie and voracious reader I've got a lot to draw on from people way smarter than me (even if I can't track back or link to all of them easily).
As to Carter and Clinton, they would actually be counter examples, in this case. They despise traditional Christians and their values. They played the part to win their votes, but they were sneering at them all along.
What I'm afraid of is someone who does sincerely believe, but takes the populist (socialist) view of someone like Bryant. That person could be truly dangerous. Did you ever see Inherit The Wind? The character of Matthew Harrison Brady, played (magnificently) by Fredric March, is based directly on William Jennings Bryant. Bryant was a true believer and had all of the evangelical Christians backing him. But it wasn't just on his fight against evolution that they backed him. He was also a rock ribbed "progressive" and "populist" and evangelical Christians, by and large, backed him on that, too. Pick him up and drop him into todays world and he would be a friend of Hugo Chavez world view, not George Bush's. Barring his own prejudices against any non-whites he would have far more sympathy with Iran's Mullah's than with Israel's Netanyahu.
We might undercut someone like that with a Clinton/Carter reminder that the recent examples of such people were frauds, but that would only stand up if he really were a fraud. What if he really believed, even though he's got it all wrong? Truly a frightening prospect.