Easily the frontrunner for the Democratic nomination will be Woodrow Wilson, having almost certainly still won the popular vote in 1916 (it isn't specified) and having only lost the election itself by the narrowest of margins, and the man seemed intent on running for a third term in OTL despite his crippling afflictions. His nomination would not be a foregone conclusion of course given he could suffer a debilitating stroke while on the campaign trail, but I personally believe it would be Wilson's health and only his health which would preclude his nomination by the Democratic Party in this universe; he is the closest to a unifying figure the Democrats have at this point, ironic as that may sound.
Most other names have been thrown out there, with McAdoo and Cox the natural frontrunners; if Wilson is able to see reason he will throw his support behind his son-in-law, which in this case might be enough to rally the required supermajority of the delegates behind McAdoo's nomination. Despite what others are saying it is also likely that Franklin Roosevelt would be named to the ticket as well... the major factor involved with his candidacy was that he carried the Roosevelt name, and it was hoped that Progressives might continue to support the Democratic ticket on the basis of association. It certainly helped that Roosevelt was from the critical swing-state of New York as well.
I think that the election will ultimately be another tossup, to some extent dependent on the economy, but also with a number of Ethno-American groups casting their votes in a somewhat unpredictable manner... the Irish certainly are not going to be throwing their support to the Republicans or Abstaining as an example, and the Germans are not going to be appreciative of the Hughes' Administrations stances towards the German Empire. The Second Mexican-American War, while a victory, is not liable to be one that rallies voters behind President Hughes given the obvious benefits from the conflict are not clear to the common man, and some may even blame Hughes for Roosevelt's death.
Edit: Suppose the voting public of the forum might have another idea however. I still contend though that the Republican Party will come out weaker with a Second Term under Hughes, and will not be surefire winners in 1924.