Lower and middle class white Americans from majority Republican states love to complain about illegal immigrants. My general impression is that the "illegal" immigration argument is a red herring and most of these people don't like legal immigrants or minorities either for that matter. One of the main arguments is that immigrants take jobs and consume resources. The whole immigrant "value added" argument falls on deaf ears even though if you go to universities you see a lot of minorities (asians) in "uncool" technical and science programs which is increasingly being neglected by the white middle class mainstream in the U.S.
So let's take into consideration the conservative argument that immigrants are the problem, what if the U.S. formed a policy to pay off recent 1st gen immigrants and 2nd gen birthright immigrants to repatriate to their parent's homeland or to an alternate homeland where they have gained a new citizenship. If you believe the whole conservative position this move could potentially save future billions in unwanted welfare burden, the "browning" of the white race, and other associated social costs.

This policy would include all 1st and 2nd generation immigrants with a special stipulation including african-americans since they were mostly brought here against their will.
What would the dollar figure be for you to voluntarily renounce?
I'd probably do it for no less than a million.

Provided that money comes tax free and with no future tax obligations to the U.S.