Unless the GOP moderates its position on illegal immigrants I doubt that they'll have a chance at the Latino vote until the grandchildren of current illegal aliens are eligible to vote.
Whiel illegal immigration is an important issue for many Latino voters, I read on numerous occasions that Latino voters also care about other issues a lot (such as healthcare, the economy, taxes, foreign policy, etc.) Besides, the Republicans lost the Latino vote even back when they were in favor of amnesty for illegals (under Reagan) or when illegal immigration was not that big of an issue.