We had two GOP presidents not enforce some laws, both named Bush. Neither enforced immigration laws to any serious extent. The open border and lack of interior enforcement are the reasons (along with Clinton's eight years) we now have to huge population of illegal aliens we have no.
Most were already here with Obama took office; he just had to gall to begin granting legal status without any action from Congress.
W totally ignored the Secure Fence Act of 2006; he had no intention of doing anything that would made a serious dent in the illegal entries into the US.