Progressivism! Periodization! and other thrills....
Now, I'm assuming that introduction has cut the readership of this post down to about three people. Which is fine by me; what I'm writing here is in the spirit of History-as-beta, and is for early adopters. But the following discussion has very little in the way of narrative or context and is meant for real history nerds. Consider yourselves warned.
So what I said was something about c19 Republican progressives being to the left of c20 Democratic/New Deal liberals, and having a historical idea about explaining this to students or readers. The first point to make is that c19 Republicans, progressive or not, were pretty much all to the left of c20, late-New-Deal Democrats, in the sense that they believed the state should have had a highly interventionist role in the economy. Let's, as short-hand, accept John Gerring's definition of c19 Republicanism as mercantilist heirs to Alexander Hamilton and Henry Clay, who wanted to use the power of the state to shape the economy to increase the health of the state.
There's a sense in which, from this angle, you can characterize Republican progressivism as Bismarckian, as a conservative effort to outflank radical movements by turning workers into clients of the state. And indeed, some progressives talked this way (see, e.g., Albert Beveridge attesting, albeit after the fact, to TR's historical significance).
Okay, now we have the idea that a statist/mercantilist party, in reaction to industrialization, might look a little radical -- might even be a little radical. This is not a terrible explanation of progressivism, at least for a first approximation. But, neither is it really satisfactory, mainly because it sets up progressivism as a response to a socialist or communist threat. Which in the main it probably wasn't. The major radical threat wasn't socialism or communism, it was populism. Maybe we should say that the move toward progressivism in the Republican party isn't so much class-oriented as it is sectionally oriented.
Let's take a second run at this explanation. How did the Republican Party change? It changed by becoming a party that appealed more to the West. The GOP had in effect to re-win the West: Benjamin Harrison and the Republican majority in the 51st Congress both drew support from the West. But between the 51st and the 56th Congress, the Republicans' ability to win the new states of the West diminished. Only once Roosevelt entered the White House did the Republicans begin to re-win those States.
So it was the West that tugged a mercantilist, statist party to the left, making it progressive. Which is one major reason American progressivism didn't really look Bismarckian -- those Westerners didn't want the same things that European workers did. (There are other reasons. I wrote a book about some of them. Did I mention this? Excuse my crass flacking, but I mean, if McDougall isn't going to net me royalties....) And as to why this set of policies were to the left of New Deal liberalism, I guess I can refer you to again to the above-mentioned post and its spinning-out of distinctions. (By the way, Casey Blake disagreed with me. And I disagreed with him. And he disagreed with me. And Geoff Nunberg disagreed with both of us, but especially me.)
For kicks, we could go a step further than this, though, and venture into the great historiographical morass of periodization. Sometimes I try to sell my undergraduates on the idea that you can explain pretty much everything that happens between the Civil War and World War II with reference to two factors: the admission of the West and the failure of Reconstruction. What's more, I sometimes say, these factors give you a really neat break point in starting the Progressive era. In 1888, the Republicans narrowly regain the Presidency and the Congress. Immediately afterward, you get both parties reaching for sectional coalitions. The Democrats launch their legal disfranchisement efforts in the South. The Republicans get the admission of six Western states, most of which are supposed to be electorally favorable to them. These sectional obligations determine what both parties can and can't do for quite a while.