The phrase "overwhelming consensus" means that the majority of people strongly agree on something or have the same opinion about a particular matter. Full definition
There is now overwhelming consensus among scientists that fossil fuel emissions cause global warming. (scientificamerican.com)
But if our social media community is anything to go by, there was a rather overwhelming consensus of what our weaknesses and shortcomings were, and how they needed to be addressed. (throughitalltogether.sbnation.com)
Thus, there is overwhelming consensus in the field that parental alienation exists and represents a very real problem. (amyjlbaker.com)