You're mixing presentation of historical fact with iconography. Even if you can build an evidence-based historical case that Woodrow Wilson was the "most progressive president" or a similar statement, your chosen line of "biggest progressive icon in American history" is immediately dubious due to the FDR meme, a horde of presently-available SJWs, etc.
Oh sure, Woodrow had his day. The world-war-I era is no longer really seen has having quite the same direct, immediate relevence to today, in the American mind, in the same way as the precipitations of depression - WWII etc do. and it is /that/ era which is FDR all over, hence FDR is the (presidential) modern ikon of progressivism at least up until Obama, in some sense, irrespective of historical fact, the anti-lynching dealmaking, etc.
Also, this thread in general really is pretty god-awful in that I've got a fucking Carter apologist.
Take this prick: , although he has correctly identified the deity aspect in our national religion, he has also failed to understand something elementary: if you don't get why, let's take our simplest examples of Washington and Lincoln, are very simply and in fact "national heroes" if nothing else, then there's nothing that can be done for you except to recommend reading some more evidence-based historical accounts.
The people writing in this thread never lived through Carter. At the hazard of an anecdotal blogpost, my father did, and he never missed an oppurtunity to remind me of how terrible things actually, really were in the country during those years: high gas prices, Iran humiliation, post-Vietnam malaise (this is the pessimism still pervasive in the popular culture of the period), the Susan B. Anthony dollar, a hideous piece of currency, etc.
Also your zeroing in on Wilson as disproof of that other guy's thing is deeply disingenuous in that you know very well that the left has its own icons, whether Wilson is now one of the polite ones or not.