Immigrants doing jobs that wouldn't get done?

I just got back from teaching a 3 week class in Spain. As part of the class we had a guest lecture on immigration to Spain. The change in immigration in Spain is incredible. 20 years ago less than 1% of Spain was foreign born now that figure is close to 15% (similar to the US). Like the US many immigrants came to work in Spain in construction, agriculture, and domestic services.

In Spain there seems to be much less blame on immigrants for negative impacts on the economy. According to our speaker the Spanish were more likely to believe immigrants were doing jobs that Spaniards wouldn't do, well that and a good social safety net.

In general I had thought, the doing jobs natives weren't willing to do isn't quite the right way to put it. That immigrants were working at wages that Spaniards (Americas) would not want to work at. However, it may also be that immigrants are doing jobs that have such low returns that no Spaniard would work for amount of income the job creates. In short imagine picking cotton creates $4 an hour worth of income, if no American/Spaniard is willing to work for $4 an hour than no one will pick cotton. Adam Ozimek demonstrates this nicely in a post with a discussion of farmers in Georgia leaving crops to rot since they can't get immigrant labor.

Of course the second part is that cotton prices will rise and so will wages, but if there are substitutes from other countries or machines can be used the potential wage may never exceed the minimum wage native workers will accept.