The general consensus at languageandgrammar.com is that the expression general consensus is redundant.
Consensus means that the majority holds the same opinion; in other words, it’s the general opinion of the group. Logically, then, not only is there no reason to use the word general in front of consensus, but it’s an error of redundancy–unless saying general general opinion does not seem redundant to you to you.
Language redundancy is a common problem in English. Part of the reason for the redundancy issue–I mean, problem (No, I’m never going to let that go, so don’t ask me to)–is a tendency to repeat what we’ve heard before rather than think about what we’re saying. We’ve heard general consensus hundreds or thousands of times, so we don’t question the validity of the two words when combined; thus, we repeat the redundancy.
I talk more about redundancy in my book; in fact, one chapter in Literally, the Best Language Book Ever is devoted to redundancy and repetition.
–Paul
Paul’s book–Literally, the Best Language Book Ever
Everything Language and Grammar 
The use of the word “general” is used with the meaning of no particular area of judgment. “consensus” then being used as a majority. So say 9/10 people like this lady’s hair color, 9/10 people like this lady’s attitude, 2/10 people like her clothes. So, you could then say “the general consensus” is, people like this lady. You are not saying all people like this lady, you are not saying that most people like this lady, you are saying that generally, she is liked. I think this is said in a way that can be understood.
This is just my thought though.
Jon P. Boone
Reply from Paul: Thanks for the comment, Jon. I believe that consensus already implies that, generally, the idea or the person is accepted, not necessarily acceptance by everyone. I would think if everyone were in support, then “unanimous agreement” would be a better term than consensus.
Paul:
Not everyone agrees, not everyone has the “liking” for the same reason. So with this debate everyone involved has their own consensus, therefor there is no general consensus.
I do not have a higher education in the English language, this is merely how I perceive it.
Thanks for the reply!
~Jon
Reply from Paul: I respect your right to disagree, but consensus means that the majority of the people agree; if the majority doesn’t agree, then there is no consensus. In the example you used, perhaps there can be a consensus for each attribute (hair color, attitude, and clothes), but, in the end, there is either a consensus that they like her (a majority like her), a consensus that they don’t like her (a majority don’t like her) or there is no consensus at all.
A general consensus is contradictory just as a general majority is contradictory.
Speaking of redundancies. . . what is your position on “scant little?” Is this a redundancy? EXAMPLES: “a scant little cup or sugar” or “he paid scant little attention to the lecture” A colleague and I have a differnece of opinion on whether or not “scant little” is a redundancy and would appreciate your thoughts. Thank you.
Scant little certainly seems redundant since the mean basically the same thing–sort of like a tiny little puppy.
What a great debate! I know I’m a little behind on this discussion but I hope to contribute another perspective.
Perhaps general consensus is a redundancy error for the purpose of clarity. Take for example, a news report on a murder scene. Lets say there are a lot of clues that lead to one particular suspect, and the cops believe they know what happened but are not releasing information. The news report may indicate a consensus gathered by authorities or maybe their own consensus on the information they have. Although, lets say this secret information was revealed to the public, it may be more clear for them to say “The general consensus is…” (general now not referring to a majority but rather which public group that creates this consensus), a clarification regarding a consensus not including/not limited to the people in position of authority over the crime (The general public).
You are all incorrect with your assumptions. The real fault is the left wall of the banana boat. From then on it has been a wave of confused crabs that cant find a place to sleep. And I thought that would be obvious.
Well Danny, I don’t see how you’re correct with your assumptions, as Crabs are made up of particles, which almost never act as a wave. Though the rest of what you said sounds nearly water-proof.