I believe that the public opinion regarding the ongoing Israeli-Palestinian conflict is that they support a two-state solution. I recall a story written about the teenagers growing up in Palestine and Israel. These teenagers were invited to a social media gathering to share their views of the conflict. Both sides of teenagers also introduced themselves to the other party and quickly became friends. They didn't understand how the views of both the Palestinian teenagers and Israeli teenagers were almost the same; that the conflict between both groups ought to end in peace and not continue. If it's supported by the teenagers within the region, it should be supported by those that have no part of the conflict.
In the United States, public opinion overwhelmingly supports a single state solution in which Israel is a sovereign nation. Given the fact that Israel is a United States ally, this makes sense. Public opinion may also be swayed by deep religious ties between the United States and Israel. Due to the religious connection, a single-state option is thought to be the only option.