If immigration laws were enforced- against both employers and illegals, many could be deported that way and more would self-deport if enforcement became standard. Other illegals could be deported as they came to the attention of Law Enforcement for other reasons. It can be done, and all it takes is to do the job that has been long neglected. First we need to secure the border, then make them want to go home by enforcing laws they are already in violation of.
It would be easier than you think, it would not happen overnight but as many were caught for other things and deported, more would leave on their own before it happened to them.
It is simply a liberal lie that there is no way to deal with those that are here other than amnesty.
It sounds like your plan is being tried in Arizona right now so we can watch and see how that goes. The only part left out, of course, is that the federal government has not secured the border.
Everyone that has commented in this thread has seen border control as a critical first step. The border could be secured very quickly. It is obvious that both Repbulican and Democrat leaders do not want to do that.
If I was going to map out a strategy, it would be to push those leaders to control the border and focus on border control exclusively. By way of an incremental approach, I would pruposefully avoid the issues of those already here illegally until the first step is done.