What if, in 1912, Theodore Roosevelt and the Progressive Republicans succeeded in defeating Taft for the nomination?
A very interesting scenario. Part of me is thinking that after 16 years in power the US would be tired of Republicans in the White House, but another part of me says that Taft Republicans didn't have the balls to run a third party ticket and thus lead to massive vote splitting favoring the Democrat. I imagine that if the race were down to Roosevelt and Wilson Wilson would emphasize his idea of the "New Freedom" more to combat criticism that there was not that much difference between his perceived "progressivism" and Roosevelt's "progressivism. I imagine that due to Roosevelt's popularity the Republicans stay in office for four more years at least.
If Roosevelt gets the US involved in World War I pre-1916 he might lose re-election, depending on how unpopular the cause for interventionism would be at the time. Personally, I think a pretty interesting scenario would be President Roosevelt be elected in 1912, stay in office for eight years after which people get progressive Republican fatigue, and at the 1920 Democratic National Convention the Tammany Democrats ultimately win in the battle with the Bryanite faction with the nomination of New York Governor Alfred E. Smith, who goes onto win a landslide victory (I imagine in the neighborhood of 57.21% Popular Vote, 420 or so Electoral Votes) while being the first Democrat in a LONG time to win less than 55% of the southern white vote, but also managing to win over 50% of the New England vote (winning 56% of the vote in Massachusetts, 54% in Rhode Island). This would result in a most interesting political landscape up to the present day.