Make it illegal not only to be an undocumented immigrant but to be the descendant of an undocumented immigrant. Since our first immigration law wasn't passed until 1875 (and that only applied to Asians) this would allow the better part of the country to be deported (including much of the Republican Party leadership) thus easing our budgetary problems substantially. It would also help latinos elect their first president.
In the alternative, we might face up to the fact that a huge number of us are here because some immigrant snuck into this country without documentation - a foul practice that began in places like Jamestown and Plymouth.
By 1860 the percentage of undocumented immigrants was higher than it is today. About that time a state legislator in Illinois wrote:
"As a nation we began by declaring 'all men are created equal.' We now practically read it, ' all men are created equal, except Negroes.' When the Know-Nothings get control, it will read, 'all men are created equal, except Negroes, and foreigners, and Catholics.' When it comes to this I should prefer emigrating to some country where they make no pretense of loving liberty—to Russia, for example, where despotism can be taken pure and without the base alloy of hypocrisy."
That immigration slouch was a Republican named Abraham Lincoln.