  Messages conveyed by media act as a major drive in shaping attitudes and
inducing opinion shift. On the other hand, individuals are strongly affected by
peer pressure while forming their own judgment. We solve a general model of
opinion dynamics where individuals either hold one of two alternative opinions
or are undecided and interact pairwise while exposed to an external influence.
As media pressure increases, the system moves from pluralism to global
consensus; four distinct classes of collective behavior emerge, crucially
depending on the outcome of direct interactions among individuals holding
opposite opinions. Observed nontrivial behaviors include hysteretic phenomena
and resilience of minority opinions. Notably, consensus could be unachievable
even when media and microscopic interactions are biased in favor of the same
opinion: The unfavored opinion might even gain the support of the majority.
