What role did public opinion play in the united states's decision to enter world war i?

It actually had a big role. The US was divided on whether to get involved & what side if so.
It helped get sympathy that the British spoke English & that the Germans were attacking the ships of Americans with the U-boats. 
The American public was furious by the Zimmerman Telegraph that proposed Germany bringing Mexico into the war and helping them regain lost territories if hostilities break out. It turned the tide against Germany in the area of public relations.