To add onto what pendragon said, Wilson at first was actually very good at combating the ethnic nationalists within his own party's ranks. You have to remember that 1916 had not only World War I in full swing, but the Easter Rising had occurred in April of that year and many Irish Americans were pissed at Wilson for his Anglophile foreign policy. Irish Independence leaders in the US went as far as to throw their weight behind Charles Evans Hughes, a Republican (the horror), because he was at least "an honorable man". Wilson, the great politician he was,
equated those leaders with unAmericanism. Now this is where reverse psychology comes in, as the nationalist publications in the US started publishing Wilson's remarks widely and proudly hoping that it made the case to vote against Wilson. However, given that "Americanism" was in vogue during the Progressive Era (Wilson, as Pendragon noted, was simply adopting Teddy Roosevelt's earlier statements and making it appeal to Democratic voters) this helped make voting for Hughes seem "UnAmerican".
The author of the weblink notes that the results are kind of vague, but I believe that Wilson's strategy was pretty successful. He was pretty close in several New England states (a rarity for Democrats even up to the 1920s), doing better in Maine, Rhode Island, Massachusetts, New Hampshire, and Connecticut than he did in New York, Pennsylvania, and New Jersey (an extremely rare occurrence). Methinks he might've won over third and fourth generation ethnic voters, particularly the lace curtains, who viewed the later waves of immigrants as a bunch of bitter radicals (kind of an "oh no we're not with them" effect) as well as a few crossover WASP types who might've felt he was more pro-American than Hughes.
However, Wilson's "Americanism" would end up backfiring in a pretty bad way later on, as the results of 1920 show.