There are already plenty of such visas for which foreigners who want to legally work in the USA can apply. I don't see any need to create any new visa program, especially one which rewards these foreign criminals for breaking the law.
I tend to agree with not rewarding lawbreakers, but.... when you have 15 to 20 million people already here, many that are here only to work, that aren't going to move out of this country without force being used, what do you do to make it right for this country?
There needs to be a process that these people can go through to become a legal worker in this country.
Not a citizen, not a permanent legal alien, but a legal temporary worker.