Which is a surprisingly easy PoD to pull off. One of the key factors in Hughes defeat in 1916 was, funny enough, his failure to meet with the highly popular progressive California Republican Governor Hiram Johnson and discuss the election campaign with him. Hughes did so assuming Johnson would support him based on party loyalty regardless while completely missing that Hiram took that decision as a personal slight and refused to lift a finger. Have Hughes meet Johnson, win him over, and pick up California and you've got Woodrow Wilson as a one-term nobody and the possibility of the Socialist Party and IWW getting the breathing space they needed.
First of all, while I agree that Hughes could have won in 1916, I think the reason he lost California is often misunderstood. It was not IMO the matter of his unintentionally snubbing Johnson. Hughes' problem with the Progressives--in California as elsewhere--was caused by his politics, not his manners. As Secretary of the Interior Franklin Lane, a Californian, said after the election: The result in California as in the whole West turned "upon the real progressivism of the progressives. It was not pique because Johnson was not recognized...Johnson could not deliver California. Johnson made very strong speeches for Hughes."
http://books.google.com/books?id=8mwoAAAAYAAJ&pg=PA227 A progressive Republican like William Allen White, though he voted for Hughes, had to admit that "Men who have gone out and made the long, tedious, and often rather lonely fight that has ended in a social revolution like prohibition, or a political revolution like woman suffrage, or the initiative and referendum, could find nothing in Mr. Hughes’s speeches to set their teeth in. He talked tariff like Mark Hanna. He talked of industrial affairs like McKinley, expressing a benevolent sympathy, but not a fundamental understanding. He gave the Progressives of the West the impression that he was one of those good men in politics—a kind of a business man's candidate, who would devote himself to the work of cleaning up the public service, naming good men for offices, but always hovering around the status quo like a sick kitten around a hot brick!"
http://books.google.com/books?pg=RA...2GyATJxoLQCQ&id=cnU9AQAAMAAJ&ots=NAJ8d3vyL7#v
Second, I just don't see Hughes's election making the Socialists a major party. True, during the war itself they might make gains, just as they did under Wilson (Morris Hillquit's showing in the NYC mayoralty race in 1917, Victor Berger's in the Wisconsin Senate special election in April 1918, etc.) and for the same reason--dissatisfaction with the bipartisan pro-war consensus. But this will be essentially a protest vote, not a vote for socialism, and will wane after the war ends. Dissatisfaction with the Hughes administration's handling of domestic affairs and of the peace treaty will benefit the Democrats, not the Socialists. The usual argument that a vote for a third party is "wasted" will again be decisive. In addition, two other things will weaken the SP. First, even if Hughes is more civil libertarian than Wilson, there will almost certainly be *some* Red scare. Second, the Bolshevik Revolution will still lead to the Socialist-Communist split that did so much to cripple the SP in OTL.