During the time the U.S. was in WWI, Woodrow Wilson put his political opponents in prison, allowed the IWW to be obliterated by mob violence, tolerated the popular abuse of German-Americans, and put the entire economy under government control, all in the name of the war effort.
Randolph Bourne, based on all this, said "war is the health of the State." H.L. Mencken, not exactly the most respectful sort himself, was put under surveillance, although it seems the government left Bourne alone.
So what if someone had concluded Wilson was a dictator in the making and needed to die? And done it?
Wilson's VP, Thomas Marshall, doesn't really seem like the strongest personality, so I can't imagine him behaving as iron-fistedly as Wilson did.
http://en.wikipedia.org/wiki/Thomas_R._Marshall
If the assassin can be traced to the radical labor movement or the German-American community, things are going to get ugly for them. Many of the abuses of the WWI era were popular hysteria, not Wilson sitting in an evil tower somewhere signing death warrants, and although there was eventually a reaction to Wilson's behavior, it did not come until later on. Most people would not be glad--they'd be upset. He is, after all, the President of the United States, and it's not like the declaration of war was unprovoked.