A big lie is a propaganda technique. The expression was coined by Adolf Hitler in Mein Kampf in reference to a lie so "colossal" that no one would believe that someone "could have the impudence to distort the truth so infamously." Hitler used the expression to criticize argued Jewish propaganda.
All this was inspired by the principle—which is quite true within itself—that in the big lie there is always a certain force of credibility; because the broad masses of a nation are always more easily corrupted in the deeper strata of their emotional nature than consciously or voluntarily; and thus in the primitive simplicity of their minds they more readily fall victims to the big lie than the small lie, since they themselves often tell small lies in little matters but would be ashamed to resort to large-scale falsehoods. It would never come into their heads to fabricate colossal untruths, and they would not believe that others could have the impudence to distort the truth so infamously. Even though the facts which prove this to be so may be brought clearly to their minds, they will still doubt and waver and will continue to think that there may be some other explanation. For the grossly impudent lie always leaves traces behind it, even after it has been nailed down, a fact which is known to all expert liars in this world and to all who conspire together in the art of lying.
—Adolf Hitler, Mein Kampf