Going after the employers that knowingly hire illegal is the only thing that will make a dent in it.
The real answer is comprehensive immigration reform, but both parties make too much money off the immigration issue, and it has been this way, all the way back to Ronald Reagan or before.
Sooner or later you have to choose between making more sensible arrangements to get the labor we need legally, or crack down on the ones that hire the illegals. Otherwise, you are just intentionally sponsoring the problem, and enticing the illegals to illegally come or stay for work most naturally born Americans do not want to do. The labor that built my pool were H1B, the pool company arranged for, every year for the pool building season in West Tennessee. But, at the same time, some unscrupulous employers use the H1B program to hire cheaper foriegn labor to replace higher paid American workers. There are problems with the system, that are not being addressed, as all businesses would like to save on labor be it farm labor that Americans do not want to do for the pay rate, or highly skilled technical labor, that did not have a large enough market in the country they came from to employ all the skilled labor being turned out, so will save American Companies money, ofter being trained on specific job by the American workers, they are here to replace. Our system is broken, not really benefitting Americans. On the skill labor side, it is definitely not benefitting American workers, though save millions in pay and benefits expenditure by American companies on technically skilled labor.