Rasmussen Reports has polling data which shows:
Just 28% of voters agree that the Justice Department should challenge the state law. Fifty-six percent (56%) disagree and another 16% are not sure. (snip) Seventy-two percent (72%) of those who rate the immigration issue Very Important to their vote disagree with the Justice Department challenge.
Arizona's idea seems to be catching on. Rasmussen also finds
71% of Mainstream voters favor passage of an Arizona-like immigration law in their home state.
It is reasonable to pursue policies that are popular with the public. Does the Obama Administration have a political death wish?
Apparently the Zogby polling organization finds essentially the same results, you can see a summary here provided by The Washington Examiner.