The solution is an easy fix for Congress
Congress isn't needed for that.
Let's say courts won't prosecute thieves for stealing cars. And police don't arrest thieves for stealing cars. So you get a giant increase in car theft. (This, by the way, is the actual situation in Seattle, WA, where I used to live. I found out when my wife's car was stolen in Seattle, and the Seattle police informed us of this information.)
You do not need new laws to fix that. You need courts that will prosecute those criminal. You need police to arrest those criminals.
This is exactly the situation with illegal immigration.
Again:
No new laws are necessary. We already have them. But our country does not enforce those laws.