I think the current crop of progressives have developed a new tactic to add to the Alinsky playbook. The additional rule for radicals would go something like "Overwhelm your opposition with issues all at once, and some of your objectives are sure to get through in the chaos." That seems to be what's playing out here. A diversion, or at least, using existing circumstances as cover for an agenda item.
With Obama seeking to cement his progressive liberal achievements in his second term he is going to want to have some signature achievement to bookend his first term Obamacare passage. What that might end up being is a political achievement - getting citizenship for millions of illegal immigrants, very likely predisposed to vote Democrat once they are eligible. Passing the current immigration reform bill floating around Capitol Hill would cement that legacy of one ominous social/governmental achievement (Obamacare) and one political achievement of a (potential) permanent shift of voter demographics to the left, ensuring progressive liberal domination for perhaps decades.
Sliding immigration reform through the Congress would be difficult were it the sole issue facing the country. But with government overreach at an all time high, and the myriad of scandals facing the administration, the president can leave the efforts on an immigration reform deal to his party and allow some sort of compromise (where Republicans once again get hosed on enforcement of laws) to others in his party. And that, is creative politics. It's not good for the country, it's good for Democrats. It's avoiding the debate on immigration, one the Democrats probably believe they can win anyway.
But while Congress and the public's attention is focused on the scandal the chances of sneaking one agenda item through certainly are no worse and possibly higher than with so many resources who believe the rule of law should apply to immigration, being focused elsewhere.
That may seem cynical and ascribing too much deviousness to the president, but I remember the days when someone in his administration was advising "never let a crisis go to waste".