The definining characteristic of the GOP is, and always was, nationalism. It has been so since its first national convention in Pittsburgh in 1856. And the easiest way to define the democrats is to look at whatever counter to nationalism is fashionable at any given moment in history. In the 1850s and 60s it was sectionalism, nowadays it seems to be internationalism.
It is a serious mistake to assume that Americans ever divide along the classic Left/Right lines as is done in most contries. You yourself have asked the pertinent question in a thread you created. If we divide along Liberal and Conservative lines, why do some poor folks prefer rightists and some rich folks prefer Leftists? The answer is that we simply don't. Which party is more economically laissez-faire, and which is more authoritarian-socialist will simply depend on externally imposed circumstances, and is easily identified at any given point in history, but you cannot simply say that Republicans are Right and Democrats are Left and thus it has always been and thus it always will be. I think there's probably a sinusoidally-varying function that can describe the extreme Left-right swings in the parties, and this function has a very long period, on the order of decades. But, the definining characteristic of the GOP has not ever changed: Nationalism. Think about it, you probably stereotype us as wrapping ourselves up in God and The Flag, right? Well, that's not far off, nor was it far off in 1860s when that was exactly the way both New York Democrats and Atlanta Democrats stereotyped the GOP then. And, maybe it was deserved, hell, what would you do, if you were Weird Al Yankovic and you were going to satirize a fight song than began with "Mine eyes have seen the glory of the coming of the Lord / He is trampling out the vintage where the grapes of wrath are stored / He has loosed the fateful lightening of His terrible swift sword / His truth is marching on." ? I mean, that's a lyric just asking to be made fun of by the Democrats.
Plus ça change, plus ce la même chose. N'est-ce pas, mon ami?
But, to answer your question, it was before the New Deal. I only caution you not to make the mistake made by the talking heads on FOX, MSNBC, and the like, who attempt to oversimplify, or to compare American "liberalism" or American "conservatism" with those concepts that are long-established worldwide.
"Twas always thus, and always thus shall be"
--Robin Williams in Dead Poets Society
Great post, Angus. Even in the 1920s and 1930s, when nationalism meant isolationism and a weak defense establishment, because a strong defense establishment would only be used for internationalist intervention, Republicans displayed the nationalism of the time.
Back then, nationalism meant that America was too good for the world, and Republicans, more than Democrats, embraced this position, and gave it up more reluctantly than Democrats when Nazi aggression forced a rethinking of it.
For a period during the Cold War, both parties were about equally nationalistic, but during and after Vietnam, liberals moved toward an isolationist brand of internationalism, if that makes sense, with the basic philosophy being that America is evil and therefore shouldn't do anything to defend itself on its own, without the approval of a multitude of coutries that are indifferent or hostile to us. That is where we stand today.
We have gone from America avoiding unilateral action because it is too good to involve itself in the evil outside world, to America should avoid unilateral action because America itself is evil. And through it all, Republicans have had the nationalistic position, while Democrats have adapted to whatever the anti-nationalistic position is.