We don't yet have explicit data on the reaction of the public to the U.S. Department of Justice's decision to file a lawsuit against the Arizona immigration law. A reasonable hypothesis is that reaction will be more negative than positive -- if the reaction follows what we know about existing views of the Arizona law.
Most polling with which I am familiar shows a plurality of Americans favor the Arizona law. Way back in late April, when Gallup asked about " . . . the new Arizona immigration law," we found 39% in favor, 30% opposed and the rest saying they had no opinion.
Fast forward to the most recent poll of which I'm aware -- a late June Fox News/Opinion Dynamic poll showing that 52% favor and 27% oppose " . . . Arizona's new immigration law."
CNN in May used this question construction: "Arizona recently passed a law concerning illegal immigrants. Based on what you have read or heard about that law, do you favor or oppose it?" and found 57% support and 37% opposition.
Attitudes about the Arizona law are highly partisan. This means that the Department of Justice lawsuit will have obvious political implications in the days ahead. Republican Senator Jon Kyl of Arizona thinks so, saying Wednesday night: "It is obviously political".
No doubt Republican strategists are at this very moment thinking long and hard about how to turn the Department of Justice lawsuit into a midterm election advantage.
Already we have a statement opposing the lawsuit from Arizona's two Republican senators, John McCain and Kyl (the former facing a tough re-nomination battle in that state's GOP primary):
"It is far too premature for the Obama Administration to challenge the legality of this new law since it has not yet been enforced. Most legal experts believe such a 'facial challenge' to the statute would be very difficult to win. Moreover, the American people must wonder whether the Obama Administration is really committed to securing the border when it sues a state that is simply trying to protect its people by enforcing immigration law."
Gallup polling shows that Republicans favor an approach to immigration emphasizing keeping immigrants from entering the country, rather than dealing with illegal immigrants already here. This is presumably one reason why Repubicans tend to favor the Arizona law. Democrats tilt the other way. But, a not-insubstantial 43% of Democrats say that keeping illegal immigrants from entering the country should be the top priority.
Still, we assume that Democratic strategists are speculating on the possibly positive impact that the lawsuit might have on Democratic chances this fall in certain states and districts with high percentages of Hispanic voters.
Gallup trend data show that Obama job approval has been drifting down this year among Hispanics nationwide. Here's an update on the Obama approval trend through June:

Stay tuned. Gallup should have a read on initial reaction to the Department of Justice lawsuit against the state of Arizona by Thursday. And we will monitor Hispanic views on Obama and the midterm elections in the months ahead.