I imagine it's possible simply by having an actual neutralist - say, William Jennings Bryan - as President.
If the US, under Presidential pressure to do so, adopts policies to "guarantee neutrality" -- ban Americans extending credit to belligerents (similar to what Bryan suggested as Secretary of State), banning belligerents' ships from US ports and US ships from belligerents' ports (inspired by Napoleonic-era US laws), refusing to recognize the right of belligerents to restrict US trade with other neutrals in any way at all (a typical position of neutrals), and banning US citizens from traveling on the ships of belligerents -- the war tilts to the Central Powers, and then a desperate Britain might manage to bungle its way into the US entering the war.
For example, under this scenario, the US will ship plenty of food (and steel, etc.) to the Netherlands and Denmark, with the locals then selling it on to Germany on credit. Cutting this off would require violating US neutrality or declaring war on the Dutch and Danes (and, logically, to avoid slightly-further neutral transshipment, the Swedes and Norwegians). At the same time, the Germans could pursue submarine warfare against Entente-flagged shipping with minimal risk of actually upsetting the US (since the ships neither stop at US ports nor legally have any US passengers on them).
Now, in general, I expect the outcome of that will much more likely be US neutrality all the way through, with an Entente defeat at the end. But the British acting desperately after the collapse of Russia and managing to bring the US in on the side of the Central Powers looks entirely possible.