Except in the all too common case where a minority has disproportionate power with which it can impose its will against a majority.  In that situation, civil disobedience is clearly in order.

As for the "too close to call" case, I need to think about it more.  What percentage of the French population was against the CPE law when it first was passed?  I guess in that case, it was not so much how many people were for or against it, but how many people were even aware of it, or cared about it.  I guess that is another constructive function of protests, and perhaps, yes, civil disobedience: raising awareness and educating the third parties about the issue.

Point n'est besoin d'espérer pour entreprendre, ni de réussir pour persévérer. - Charles le Téméraire