We need to change the citizenship law to reduce the incentive for this behavior.
We need to get a law passed with MANDATORY jailtime for any EMPLOYER who hires them. That's all we need to do. Cut off the job supply and watch the invasion disappear.
Employer sanctions are the most effective way to stop "regular" illegal immigration. Additional border and port-of-entry controls are also needed, however, to complement employer sanctions and to thwart intending criminal and terrorist illegals who may not ever have (formal) U.S. employers.
Don't expect much of this, of course, under the current President.