The people who keep the wages low are the people who pay low wages. And in the case of people paying wages that are lower than the statutory minimum, the authorities who fail to catch them.

No, the people who are willing to accept the low wages are also keeping them low. That's why unions don't like people who cross picket lines and go to work when the union is on strike. But the point that I was trying to get across is that this is how our present government wants things. They are using the illegal status of the immigrants as a tool to keep wages in this country low. And this is why it is different than the situation you're describing in your country.

The solution to this problem is not to blame the immigrants, but for the government to stop using them as a tool of oppression, which means we need to elect people who will correct this problem. The Republicans will not do this. The Democrats might or might not, but the chances are far greater that they will. So to tie this into what Obama said: if people allow the Republicans to suck them into voting for them based on manufactured xenophobia (which is what the Republicans do), they will be voting against their own economic interests.