Red herring. This means exactly what you think it means: introducing irrelevant facts or arguments to distract from the question at hand. For example, "The opposition claims that welfare dependency leads to higher crime rates -- but how are poor people supposed to keep a roof over their heads without our help?" It is perfectly valid to ask this question as part of the broader debate, but to pose it as a response to the argument about welfare leading to crime is fallacious. (There is also an element of ad misericordiam in this example.)
It is not fallacious, however, to argue that benefits of one kind may justify incurring costs of another kind. In the example given, concern about providing shelter for the poor would not refute concerns about crime, but one could plausibly argue that a somewhat higher level of crime is a justifiable price given the need to alleviate poverty. This is a debatable point of view, but it is no longer a fallacious one.
The term red herring is sometimes used loosely to refer to any kind of diversionary tactic, such as presenting relatively unimportant arguments that will use up the other debaters' speaking time and distract them from more important issues. This kind of a red herring is a wonderful strategic maneuver with which every debater should be familiar.
http://www.csun.edu/~dgw61315/fallacies.html