Not so modest and not so easy to shove through Congress. The Supreme Court might do something about anchor babies if the the right lawsuit makes it that far...
But how? The SC is only there to interpret the constitution and the language in the 14th amendment is very clear. Quite frankly, though I do not like outcome/consequence of the verbiage in the 14th amendment, I do not want a court that can willy-nilly find a way to interpret the meaning of that particular amendment in any other manner. In my view, the only sensible thing to do is to try and amend the 14th amendment by adding some key words -- key words that are carefully written so as to avoid other consequences.