Your solution, which is obvious to anybody with one good eye and a grain of sense, just plumb evades the so-called "leadership". Republicans are going to lose bigger than hell over this and nothing of the conservative agenda will ever pass again because we will have a flood of Democrat illegals given the right to vote. It ain't gonna be pretty from here on in.
The GOP seems utterly oblivious to that fact that A) they have no chance whatsoever of winning over millions of welfare-seeking (or already welfare-addicted) illegals, many of whom believe that the U.S. is Mexican property, and B) their traditional/patriotic/conservative base is taking a hard look at other (third party / Ind.) voting options.
The establishment GOP's stance on illegal immigration is a lose-lose propostion for them. ....and for the country.