Fining employers for hiring illegals would probably do more than anything else to end illegal immigration. I'm not so sure about sending them to jail, as the jails are already full. We need to save the space for violent offenders.
In addition to that, there needs to be a way in which people can come here to work and live legally.
I'd send those who are already here back home to get a green card, along with all of the rest who would like to come and work.
Sanctions against Mexico would just result in more poverty there, and a greater incentive to sneak across the border. Further, illegal alien and Mexican are not synonyms.
People who work, pay taxes, raise families here are assets to this country and should be allowed to come. We should be able to do a background check first and screen out felons, druggies, and gang bangers. We also should be able to limit their numbers to what we can absorb.
But, alas, the current practice of admitting whoever is able to elude the Border Patrol and survive the desert will most likely continue, resulting in cheap labor, exploitation, and more people dying in the attempt come.