The Republican Party was originally formed to push for the abolition of slavery. Abraham Lincoln is now recognized as the icon of the early days of the Republican Party.
What happened to the Republican Party in the post-slavery days given that it lost its original purpose? How did the Republican Party become the party of big business?
At what point did the Democratic Party become the more liberal party? Was it during the FDR administration and the New Deal? Was it during the JFK administration and the Civil Rights movement? Were Dewey and Eisenhower liberals? Were both major parties liberal during the 1932-1960 period?
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