Your typical WASP swing voters are hardly influenced by immigration policy, by itself. They usually either take a stand on moral grounds , i.e. abortion, gun-control, same-sex marriage etc., or ideological grounds like lowering welfare benefits, cutting taxes etc.

There are very, very few such voters who might say "I'd definitely vote for Obama if it was not for his stance on immigration". That number is probably negligible in comparison to the swing Latino voters the president can get by actually doing something about CIR.

Frankly, the majority of voters is uneducated, as far as both schooling and candidates' political stance, are concerned. As long as CIR doesn't pass at the end of next summer, right before the elections, most 4-5th generation US citizens won't even remember what the immigration reform actually pertains to, while in the Latino, or any other large immigrant community, immigration is a very hot issue. Any info about immigration usually ends up on the front page of foreign newspaper in the US. If something immigration related actually does pass, it will resonate in that community all the way to the election day, and the lack of education of such voters won't even matter because they will constantly be reminded of who did what and who they should vote for.