The phrase "virtual unanimity" means that nearly everyone or almost all people agree on something. It suggests that there is overwhelming consensus or a very high degree of agreement on a particular matter. Full definition
Last night, the House of Commons did a remarkable thing: on a contentious and vital issue, it found virtual unanimity. (conservativehome.blogs.com)
Despite virtual unanimity among scientists that climate change is real, and that it is caused by human activities, people who cast doubt on climate science continue to dominate the debate. (nexusmedianews.com)
The treaty nations maintain with virtual unanimity that they did not agree to extinguish their rights to their traditional lands and territories but agreed instead to share them in some equitable fashion with the newcomers. (humanrights.gov.au)