Are all these people going to go on unemployment and welfare if they can't find a job ?
The smartest way to combat illegal immigration is to dry up the incentive - employment - and go after the employers. Make it hard enough for them to get jobs and they will self-deport and fewer will come over. If someone is not willing to crack down on employers and provide them the means to determine if a person is legal or not - then they are not serious about fixing illegal immigration.