The apples-to-apples comparisons we have are more mixed: Republican support in the mid-January AP/GfK poll jumped to 53 percent from 31 percent in 2010. The latest ABC News/Washington Post poll moved to 42 percent Republican support for a path to citizenship from 37 percent in November 2012 (that’s inside the margin of sampling error). The CBS News poll did not move at all, finding 35 percent Republican support in both its December 2012 and late January 2013 surveys. And Quinnipiac polls, released on Thursday and in early December 2012, both found roughly 40 percent of registered Republicans support a path to citizenship and just more than 10 percent support legal status without citizenship.

An uptick in Republican support for a pathway to citizenship could be statistical noise. And even if it is real, it could reverse itself. Some political science research suggests that anti-immigrant attitudes increase when immigration is in the news.

But there are reasons to think that immigration, over all, has become less of a hot-button issue. A Pew study found that the number of illegal immigrants living in the United States has dropped since the 2007 push for change. Another Pew survey found that only 44 percent of Republicans see dealing with immigration as a top priority. That’s down from previous peaks of 69 percent in 2007 and 61 percent in 2011.