Given the past and the race of the current president, they might have no chance at blacks for the foreseeable future. But some version of immigration reform would help them appeal to Hispanics; maybe they don't offer amnesty but it seems like trying to outright deport illegals is killing them among Hispanics. I also think it would help for them to distance themselves from some of the more inflammatory conservative pundits, but they might not be able to do that.
There are other issues by which to win Hispanic support that don't involve abandoning their own base on a key issue.