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Use of the expression (Big Lie) by Hitler
The source of Big Lie technique, from Chapter 10 of Mein Kampf:

... 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, vol. I, ch. X[1]

Use of the expression by Goebbels

Later, Joseph Goebbels put forth a slightly different theory which has come to be more commonly associated with the expression big lie. Goebbels wrote the following paragraph in an article dated 12 January 1941, 16 years after Hitler's first use of the phrase big lie, entitled "Aus Churchills Lügenfabrik", translated "From Churchill's Lie Factory". It was published in Die Zeit ohne Beispiel.

That is of course rather painful for those involved. One should not as a rule reveal one's secrets, since one does not know if and when one may need them again. The essential English leadership secret does not depend on particular intelligence. Rather, it depends on a remarkably stupid thick-headedness. The English follow the principle that when one lies, one should lie big, and stick to it. They keep up their lies, even at the risk of looking ridiculous.