I don't know what you mean by peacefully. If it is made known that we will track down and deport visa overstays, many will leave on their own volition. It is not a matter of them acknowledging anything. This is the practice around the world. The penalty for overstaying one's visa is deportation and a ban on future reentry. These are the consequences for violating the law.
I believe the rest of them will be a difficult undertaking with no cooperation and much Democrat interference at every turn.
It is the law of the land. The President already has the legal authority to do it. He doesn't need Congressional approval.
I thinking the scale of visa violations is massive, in the several millions, that where allowing all of them to go without a fight is best, but many are going to fight it, and some with the Democrats and their lawyers in tow.