I think the easiest solution is to go after the employers. Once people stop hiring them, the incentive for illegals to stay here will disappear. I don't think there will be any way to convince illegals to register with the government, unless it is tied into some amnesty or guest worker plan.
Yep punish the people who do good things such as grow food and build buildings and create wealth.
Everything old soviet is new soviet again.
The problem is large enough to warrant multiple, simultaneous steps.
Build the fence. Hire even more border agents. Put the UAVs up monitoring our borders, too.
Likewise, encourage our Southern neighbors to step up the enforcement of their own Southern borders (Mexico hates illegals coming up North from below them).
In the meantime, that still leaves 12+ million illegals here. Rounding up 12+ million criminals who are living off the grid here will be difficult.
A plea bargain is worth considering if it reduces this level of difficulty. Such a plea bargain should be acceptable to both sides.
That too.