The phrase "a widespread consensus that" is correct and usable in written English.
It can be used when discussing a general agreement or shared opinion among a large group of people on a particular issue or topic.
Example: "There is a widespread consensus that climate change is a pressing global issue that requires immediate action."
Alternatives: "a broad agreement that" or "a general consensus that".
Now there is a widespread consensus that these connections are in constant flux.
John McCain has promised to postpone immigration reform until there is a "widespread consensus" that border security has been attained.
While there's a widespread consensus that GM crops are safe, there are valid and lingering questions about the environmental and social impacts of GMOs.
But there is a widespread consensus that consumers will develop a taste for getting up-to-the-minute data on traffic and movies and sports and even news while they are on the go.
There is a widespread consensus that the government's policies of pursuing wars in Iraq, Afghanistan and the Middle East have led to an increased threat of terrorism and increasing division between communities.
So just two weeks ahead of a meeting of the Group of 20 economic powers in Toronto, there is a widespread consensus that grand stimulus programs are a thing of the past.
There is, however, widespread consensus that: WCF is a complex, multivariate subject on which there is inadequate research adequately (Bitchener and Ferris 2012).
Among economists, here in China and abroad, there's a pretty widespread consensus that China needs to move from an export-driven growth model to a domestic consumption-driven one.
As someone born at a time of widespread consensus that human slavery was one of history's most despicable and shameful practices, I've always been intrigued by the realization that, during the life of my great-great-grandfather, there were a significant number of otherwise intelligent and sensitive white Americans and Europeans who apparently did not see it that way.
The fact that the administration is now pursuing such a course reflects the widespread consensus that the President's signature anti-foreclosure program has been a disappointment, leaving millions of American households vulnerable to losing their homes in the face of persistently high unemployment.
For example, when there's widespread consensus that a given company will perform well and their stock price will rise, there can be opportunity in doing the opposite, taking a short position, because the belief is already priced into the stock -- all the money that will be invested in the stock, already has been, so the only change will be if the belief changes and people start selling.
