The last time Congress tried to pass law(s) against "birthright" citizenship was 10 years ago in 2005. And legal to be executed under the 14th Amendment, Section 5, and US Const., Article 1, Section 8.
"GOP mulls ending birthright citizenship "
http://www.freerepublic.com/focus/news/1515559/posts
"House Conservatives Want End to Birthright Citizenship"
No every year for a decade there have been bills proposing the elimination of birthright citizenship. Currently, there is one in the Senate sponsored by Vitter and one in the House by Steve King, HR 140