Early on in Texas District 11's Representative Mike Conaway's political career one of his pet issues, as told to audiences at speaking engagements, was the problem of anchor babies. And in fact, in 2009 he co-sponsored, H.R.1868, The Birthright Citizenship Act, which sought to clarify the 14th amendment. But the bill died.
The issue has risen from the ashes, thanks to Donald Trump and others. Steve King currently has a bill in the works, The Birthright Citizenship Act of 2015. Govtrack.us gives that one about as much chance as the previous one.
Nevertheless, Representative Conaway's website has gone silent on the birthright issue. It must be tough for an establishment Republican to watch Donald Trump steal his issue.