Hispanics tend to vote Democratic anyway. That's the reality. Not as overwhelmingly as black voters, but they're still a democratic voting group nationally, with Florida being a bit different.
Right now, Dem politicians are pandering to hispanic voting groups big-time. And the House resolution pretty much created whatever animosity might exist anyway against the GOP. The cat is out of the bag.
Trying to win hispanic votes by pandering on the immigrant issue will never work, because the Dems will always pander more. I think a responsible position that emphasizes border security without demonizing all illegals won't alienate hispanic voters who otherwise would support the GOP, and will win a lot of other votes as well.