Also known as the false dilemma, either-or fallacy and black and white thinking . The argument is presented in such a way to as to suggest that there are only two possible options. The arguer then presents their evidence against the disfavored option and so it is then reasoned that the favored option must be accepted. It takes the form of: Either X or Y is true. X is false so Y must be true. This sort of reasoning is fine as long as there are truly only two possibilities, but if other alternatives exist then it is possible that both X and Y are false.
The false dichotomy may be used intentionally by an arguer to influence a debate or to force a course of action. An example would be: "Ann, I need you to donate $15 to the starving children of the world fund, unless you don't care about starving children." The two options presented are that Ann gives $15 and cares for starving children or she doesn't care for starving children. Of course a third possibility is that Ann cares for starving children but cant or doesn't want to give $15.
The false dichotomy can also arise unintentionally simply by not considering additional possible options. For instance "Silvia Brown can either talk with the dead or she is a con woman. She passed the lie detector test I gave her so she can talk with the dead." Of course another possibility is that she cannot talk with the dead but truly believes she can.
I see this kind of thinking all the time in political discussions. This is probably due to the fact that we only have two major parties, which I think tends to have a polarizing effect on our thinking (Regulation is good or regulation is bad, welfare is good or welfare is bad).
Other examples would include: "If we don't raise taxes, our government will collapse", or "you are either with us or against us" or "Which would you rather have, better schools or lower taxes".