It's easy enough to fix the 14th amendment to bring it in-line with reality. Congress just has to get the balls to do what's right, and not pander to the Latino vote.
Not pandering to the Latino vote means being a minority for years to come. Check out what happenned to the Republicans in California after Pete Wilson suggested denying services to immigrants. Do the Republicans really want to repeat this all over the nation?
You forget, I could care less about "parties" and care more for what is right for the country. If the Republicans would explain why they are for this, and teach the citizens who are unaware/uninformed (which is most of them) the situation, then it won't negatively impact them much than if they did it without an discussion with the public.