Perry is against E verify.
His stance is that it is ineffective and only adds to regulation of business.
As far as anchor babies go you will have to get 2/3 of congress and the senate to rescind the national immigration act that passed into law 46 years ago by an 82% margin.
Immigration and Nationality Act of 1965 (Hart-Celler Act, INS, Act of 1965, Pub. L. No. 89-236)[1] abolished the National Origins Formula that had been in place in the United States since the Immigration Act of 1924. It was proposed by United States Representative Emanuel Celler of New York, co-sponsored by United States Senator Philip Hart of Michigan and heavily supported by United States Senator Ted Kennedy of Massachusetts.[2]
Article about the Act and Kennedy’s involvement:
http://en.wikipedia.org/wiki/Immigration_and_Nationality_Act_of_1965
Article about an anti illegal program that worked:
http://en.wikipedia.org/wiki/Operation_Wetback