The only way amnesty could work in the United States is if you granted amnesty in one large swoop of individuals who have been inside of the United States longer than ten years as a minimum requirement granting instant citizenship. That would give legal citizenship to millions of people.
Everybody who fails those requirements would be deported. To smooth that transition as a parting token given them thousands of dollars in financial compensation to resettle back into their nations of origin.
With amnesty passed nationwide immediately halt all foreign immigration and seal the national border up immediately. Initiate nationwide legislation that no bills or laws for immigration amnesty can pass for the next fifty to sixty five years in a moratorium allowing time to absorb the millions of new citizens within your national population as a result.
The best method of political compromise I can think of.
