No, Jimmy Carter didn't really lead Ronald Reagan for most of the 1980 campaign, only to have Reagan suddenly surge from behind at the last minute (John Sides really took care of this a while ago).
But, you know, what's a campaign behind in the polls supposed to do? Of course they're going to find some historical evidence, no matter how dubious, to show that everything is going exactly as they want it to be. And they better do that; it would be irresponsible not to. After all, for a candidate who is not all that far behind but would need some external shock to change things (which is increasingly where it appears Mitt Romney is right now), the trick is to keep the situation from imploding so that even a significant external shock wouldn't be enough. Donors need to be told to keep giving, volunteers have to be inspired to keep volunteering...even the paid staff needs to be given some reason to believe they're not wasting their time.
It's not just the possibility of winning, either; even a doomed campaign, a Dole '96 or a Mondale '84, needs to maximize whatever vote it can get in order to avoid pulling the rest of the ticket down with them.
The Reagan/Carter/1980 thing is really just a twist on the old idea that every losing candidate in my memory would pitch themselves as Harry Truman, ready to hit the stump for personal campaigning that would turn the whole thing around. I guess the 1980 version of it appeals to Republicans because it's Reagan...and I suppose there's at least some vague analogy in the economic situation, although not really.
There's another piece of this, which is the constant partisan arguments about individual polls -- that the sample is wrong, or whatever.
The key is that unless one is that these are really pretty innocent lies. I mean, it's fine for reporters or pundits to call them out on it, but it's not on the same scale as, say, lies about policy or about the opponent's character. Just stipulate that both sides are going to interpret the polls in whatever way serves their interest, and that no campaign is going to admit that it has little or no chance to win. It's not lazy mendacity for Republicans to dredge up this particular myth; it's really the only responsible way to run a campaign.