Economics 101: Does amnesty decrease income gap?

So we have previously disproved that high taxes and unions do not improve income gaps, as the three states with the highest taxes, and forced unionization, were the three states listed here:

1. Arizona
2. New Mexico
3. California (top marginal tax is 13%)\

Interestingly enough, another means liberals use to try to decrease the income gap, to create fairness between the rich and poor, is amnesty.  The problem is, that all three states with the highest illegal immigration rates are the same three states listed above.  

So, it would appear that in order to decrease the income gap would be to do the opposite of what liberals propose, and that would be to lower taxes, get rid of unions, and get rid of illegal immigration.  

Could you imagine a politician proposing this?