A dilemma is a schematization of a situation as an alternative whose terms are equally undesirable. Used as an argumentative strategy, the dilemma corresponds to a case-by-case refutation, consisting in cornering one’s opponent by showing that all his or her lines of defense lead to the same negative conclusion:

Either you were aware of what was going on in your services, and you are an accomplice, at least passively, of what has happened, and you must resign. Or you were not aware, then you do not control your services, and you must resign. Either way, you will have to resign.

A dilemma can be rejected as poorly built, as a false dilemma, an artificial radicalization of a more complex opposition, which can be reconstructed in order to show that there is a third way out of the dilemma, S. Case-by-case.

If I have clear and strong support from the citizens to remain in office, the future of the new Republic will be secured. If not, there can be no doubt that it [the new Republic] will immediately collapse and that France will have to endure, this time without remedy, a confusion of the State even more disastrous than that which it once knew.
Charles de Gaulle, 4 Nov. 1965 Speech, announcing his candidacy for the December 1965 presidential election[1]

This relatively common practice of framing the political situation can be rephrased as the slogan “it’s either me or chaos”. A supporter of the speaker will take this statement as offering a realistic clear-cut choice between good and evil. An opponent will reject it as an arrogant and inadequate means of pressure. Undecided citizens may see it as the expression of a real dilemma, a choice to make between two equally undesirable options.

[1] http://fresques.ina.fr/jalons/fiche-media/InaEdu00101/de-gaulle-Fact-de-candidature-en-1965.html] (11-08-2017). The last phrase alludes to the June 1940 military rout.