American politics would probably have developed a lot differently. The Great War broke the Socialist Party of America in a combination of state directed terror and their own strenuous opposition to the war, and avoiding that means that the Socialists are probably going to become much more influential on the federal level in the 20th Century.
Woodrow Wilson most likely will not win a second term as President. With many on the left giving their vote instead to whomever the Socialist Party nominates, and Wilson without a war to use to his electoral advantage, the ensuing vote split probably gives Charles Evans Hughes the Presidency come 1917. Assuming OTL's 1912 Socialist showing doubles to say, 12% in the 1916 Presidential Election, we also probably get a fair number of Socialists elected to the House of Representatives.
President Hughes probably has to deal with calls for social reform from a tripartisan progressive alliance in the House, and will most likely yield to a lot of these demands. The 1918 midterm elections yield another strong showing for the Socialist Party, which has gobbled up Northern Democratic seats and is beginning to break down the urban party machines. No Russian Revolution (perhaps thanks to the Czar modernizing Russia more quickly and avoiding reaction) means that the Socialists don't face the devastating right-left split they faced IOTL as well, so a synthesis of revolutionary and reformist ideas probably emerges as a result, with reformism eventually winning the day.
The 1920 Presidential Election between Hughes (R), Cox (D), and Debs (S) yields another doubling of the Socialist vote, to 24% of the popular vote and the capture of a few electoral votes for the first time. The Democrats in the North are in serious, perhaps irreversible, decline by this point, and President Hughes is again saddled with a reformist Congress.
A world-wide recession in 1921-1922 gives the Socialist Party more members in the House than the Democrats for the first time, though they are still outnumbered by the Republican Party. In the 1924 Presidential Election, a tripartisan alliance of progressives, lead by Robert M. La Follette, work out an electoral alliance to contest the Presidential election that year. La Follette (and his running mate, Burton K. Wheeler) will run on a 'progressive' ticket supported by and endorsed by the Socialist Party, in hopes of finally breaking through and getting into the White House. Facing down Republican candidate Calvin Coolidge and Democratic nominee John W. Davis, the Progressive/Socialist ticket manages to throw the election to the House of Representatives for the first time in a century, where an alliance of progressives from all three parties makes La Follette President.
La Follette's Presidency is short-lived (he will die in the summer of 1925), but he is able to enact a flurry of reforms, mostly equivalent to OTL's New Deal social legislation. Child labor is finally banned outright, a system of Social Security is established, minimum wage laws are put on the books, and a few progressives are put on the Supreme Court. La Follette's death puts Burton K. Wheeler in the White House, a man who is every bit as progressive as the man before him, but not so skilled at working with Congress. The 1926 midterm elections reduce the number of progressive non-Socialists significantly, and by the 1928 Presidential Election, the Republicans have mostly exiled remaining Republican progressives while Democrats have become a full-throated Southern party. Wheeler, without the same political prowess as his predecessor, is unable to win renomination from the Socialist Party, which nominates Norman Thomas instead. Thomas goes down in defeat to Calvin Coolidge, and the Democratic nominee, Al Smith, comes in a distant third.
President Coolidge deals with a minor recession in 1929-1930 that gives the Socialists control of the House, though they lose it once again when Coolidge is re-elected in 1932, defeating the Socialist and Democratic candidates by a good margin. Coolidge dies however in 1933, leaving the White House to Vice President Frank Lowden. Lowden promotes deficit reduction and fiscal conservatism, but is otherwise a rather boring President with not much going on in terms of real legislation. Lowden loses the House to the Socialists in 1934, and in 1936, the Republicans fail to renominate him, instead choosing Kansas Governor Alf Landon. The Democrats nominate popular former New York Governor Franklin Roosevelt, and the Socialists nominate Norman Thomas, who campaigns on making America 'a shining city on a hill for the working class'. Thomas is swept into office with the first majority for a Socialist candidate, and further, the Socialists take control of the House and the Senate for the first time in their respective history...