My opinion is you cannot expect the federal government to take the lead on the issue of illegal immigration. Individual states are the ones that must begin making it more difficult for illegals to work and live in that state. There are various methods to accomplishing this but as with anything else it will require money and enforcement.
It all needs to start with employers. Businesses must be held accountable when someone they hire is not legally allowed to be employed in the US. Unfortunately this will cause many small businesses to suffer but it is a price that must be paid in this case. Landlords also should be required to show evidence that their rentee has the proper documentation. It really doesn't take anything more than copying a work permit and keeping it on file. Enforcement agencies should constantly monitor local businesses and ensure they are complying with employment standards. It's not hard to find out which businesses should be monitored, everyone knows where illegals work.
There is no need to involve the federal government in such easy and small scale efforts. The incentive to skirt the law by those who employ or house illegals must be removed before the problem becomes manageable.