Perhaps TR wins, the Republicans never fully recover and are forced to either join the Democrats, or the Progressives or remain members of a third party that has some local offices and some senate seats. If its in 1912, the US could throw its weight in earlier, avoiding the Russian Revolution with the First World War ending in 1916.
If he wins in 1916, then he could take the sides of the Whites in the Russian Civil War keeping the Soviets from coming to power. Eventually the Socialist and Progressives will merge, they did in OTL, though its not exactly the same Progressive's, perhaps FDR will run on the Progressive ticket in 1932 and the Socialist throw their lot in behind him, during the 1950's the two parties basically merge. The Progressives will then be America's Social Democrats. The actual Democrats will remain the conservative party but more like their pre-1960s party. Liberals in the north, conservatives in the south.