Here's something to consider as you hear talk about dumping the 14th Amendment to end the "anchor baby" problem: our Congress couldn't muster enough votes to add a Constitutional amendment banning flag burning, something that enjoyed much broader support.
Progressives often talk about our Constitution as a "living, breathing" document, which is true if you disregard the tall hurdles needed to change it. Our framers rightly set the bar high to keep it from being polluted by the whims of current politics and politicians. With the exception of Prohibition, they have succeeded. Court decisions and executive branch actions ripping up the Constitution are a different issue.
I don't expect the talk of repealing the 14th Amendment to get very far. Perhaps there might be a token vote, something only of value to a political resume or a defense in an ideological purity test.
My question is whether the Supreme Court will get into the issue if somebody brings an anchor-baby case. I have read that in United States v. Wong Kim Ark 169 U.S. 649 (1898) the high court didn't completely resolve the question of whether children born to illegal immigrants in the U.S. are legal citizens. With the high court likely to take up Arizona's SB1070, I wouldn't count it out.