Immigrants don't just "take" jobs. Their presence also creates new ones. It's not as though people come here, go to work, and then never put money into the economy.
but it is true i think, that immigrants do take jobs away from the lower-skilled demographics, because they may be willing to take on a lower wage than their native counterparts. The influx of new demand due to immigrants is going to be slower to materialize as wealth to the upper-eschelons of owners, which is then slower to trickle down to more hires/jobs to meet demand. Therefore, in the immediate future, the natives are less well-off.