The phrase "overwhelming majority" means that a large or significant number of people are in agreement or favoring a certain decision or opinion. Full definition
For overwhelming majority of the people it is once in a life time trip for which they have saved all of their lives. (religion.blogs.cnn.com)
Players will tell you this, coaches will tell you this, and a huge overwhelming majority of all fan bases will tell you this. (sbnation.com)
While it might account for perhaps even an unusually large percentage of elected officials being white males, it does not account for the ridiculously overwhelming majority. (politics.stackexchange.com)