immigration vs outsourcing

I was listening to 90.1 today, and I heard a piece against big corporations outsourcing jobs overseas, and taking away jobs from the average american. Isn't that part of the fear the conservatives express about letting in immigrants? how they're coming in and taking our jobs away. Its odd, the "conservatives" are pro outsourcing, anti immigration. and the "liberals" are pro-immigration anti-outsourcing. It's an interesting world...