They're already here. Can't do anything about that. If you give them amnesty, they have no reason not to demand the same sort of wages that non-immigrant workers expect. There's no fear of deportation, so employers have lost that leverage.
On this issue I was speaking about the Rust Belt in particular here, where almost no immigrants have settled to this point. A sizable portion of the industrial workers are legitimately worried by amnesty because they believe (rightly or wrongly) that there will be more immigrants with it than without it, or that more future immigrants will come because of it to take their jobs.
Don't get me wrong; I agree amnesty is necessary at this point. But a whole lot of people back home disagree with that statement and racism and xenophobia have little to do with the reason. The reason why I mentioned immigration here is because it is an example of why working class whites may believe it is the Republicans who are looking after their interests rather than the Democrats, which is at the end the day the real reason why many of them vote Republican, not simply to express their outrage at the Democrats for having offended them.