In terms of U.S. actions, we obviously see an earlier U.S. troop presence in Europe.
As for the 1916 election itself, I suspect that Wilson would get a boost due to the surge in patriotism--similar to what George W. Bush experienced after 9/11 in our TL.
First, though - WIlson campaigned on "He kept us out of war", and by pointing to Roosevelt as a warmongering influence in the Republican Party. If the US
is at war, both of those themes disappear.
Second, one must examine whether the DoW would become a partisan issue. Would Wilson decide on it? Would Republicans then oppose it?
OTL, Republicans straddled the issue. Hughes called for greater preparedness, but criticized US intervention in Mexico, and Roosevelt was kept under wraps to a degree.
A third point - if there is a push for war, would this boost the vote of the antiwar Socialist Party? Would anti-war Progressive Republicans (such as Jeannette Rankin of Montana, or Robert LaFollette of Wisconsin) bolt to the Socialists, or launch a last-minute anti-war candidacy? The OTL Republican straddle would be impossible.