Everybody has a lot to say about the increasing levels of partisanship in U.S. politics. Democrats blame the Republicans, Republicans blame the Democrats and Independents blame the two-party system just because they're special snowflakes. However, partisanship hasn't always been such an issue; it really began under FDR and accelerated through the 1960s under LBJ.

American political history and demographic change has driven this increasing partisanship, but put very simply it's because the parties have become much more ideologically cohesive. There's much less room for moderation, although that isn't to say that efforts aren't being made.

The Blue Dog Democrats (DINOs), who held enough power in Congress as late as 2010 to make Obama drop the public choice option from the ACA, are essentially dead. The tax-and-spend liberals in the northeast and on the west coast (think Ted Kennedy and Nancy Pelosi) have clashed with the Blue Dogs, but their eminence in the party is what has allowed the Republicans to paint them as the party of the poor and of the minorities. With the defections to Reagan, and the turning of the south into a Republican stronghold, the New Democrats--formed under Clinton, Gore and the DLC--tried to shift the party closer to the centre with a more business-friendly orientation. The party has, since these shifts, oscillated between the old-style, tax-and-spend liberals and the New Democrats.

The Republicans have seen less factionalism within their own party, but it's increased in recent years. The Rockefeller Republicans, the compassionate conservatives and the Main Street Republicans all had an uneasy coalition until 2008. The "Reagan Coalition" of all the divergent factions--which was given a boost in 1994 by Newt Gingrich--died out when Obama was elected, and since then the Tea Party have encouraged their shift to the Right. The number of Rockefeller Republicans has declined, not least because of defections like that of Arlen Specter's in 2009.

Even the Tea Party, however, has essentially died out. From 61 congressional members in March 2011, the Tea Party Caucus is essentially defunct. With the failure of Mitt Romney in 2012, Reince Preibus--joined by Jeb Bush and Colin Powell--began calling for a party reform to make the party more inclusive and attractive to young people, women and minorities. However, there's no strategy for moving ahead without alienating the traditional Republican voter-base.

All of these shifts towards ideological homogeneity have resulted from demographic changes beginning in the 1950s, and electoral processes like gerrymandering, which solidify party lines and make it politically expensive for House or Senate members to make compromises or look to be weak.

I rushed this, somewhat, so if anybody has any questions I'll be happy to take them.

TL;DR:

Started long before Roosevelt.

Looking at the similarities between Teddy and Woodrow Wilson--not really. Of course there were differences, the Republican Party was founded in direct opposition to the Democrats, but the divergence was nowhere near as substantial as they have been in recent years.