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The answer is more absurd than first thought:

As the radio program "This American Life" reminded its audience on Tuesday, there is an argument to be made that the term self-deportation was invented in 1994 by two Mexican-American satirists, Lalo Alcaraz and Esteban Zul. That year, "sickened" by a ballot initiative known as Proposition 187, which aimed to prohibit illegal immigrants from using state-run hospitals and schools in California, the comedians began posing as conservative activists who backed the measure.

From an interview with "Daniel D. Portado," a character created by Alcaraz and Zul:

I founded [in 1994] the group "Hispanics For Wilson", a GOP support group of Governor Pete Wilson. Wilson correctly wanted to chase all the illegals out of California after they were done mowing our lawns, but before payday. Our first event was the 5K Border Fun Run, where we issued a press release calling for illegal registrants to sign up for a one way 5K run over the border and into Mexico. We even offered free running shoes for each participant willing to self deport.

Aforementioned TAL episode here.