What is your definition of low-skilled, by the way. That is also revelant for this discussion. Are you implying the government of the United States is supposed to only admit into the country those who have a college degree or those who can prove to have skills and formation over the average of the rest of the country? Because that would be quite a radical thing to do, and besides, that would not solve the problem of the implicit racism which exist within American society nowadays.
Are border patrol officers supposed to ask people entering illegally into the USA whether they have profesional qualifications before even asking if they have reached the border seeking for asylum, or whether they are being politically prosecuted in their home countries?

One needs to be careful with those scenarios before creating a dangerous precedent.