I don't think so. What I'm thinking is that "state green cards" would let you live in one state, and your residence will be checked up on periodically. If you don't live there, or if you're found in another state without a visa, you become an illegal immigrant, and fall under the purview of the federal immigration services.
This has very little negative changes- since many/most illegal immigrants are here on overstayed visas (anecdotally, every one of the illegal immigrants I know), and because travelling from a state into inner states is so easy, it doesn't make enforcement particularly harder. Since immigrants have a readily available alternative in the states that want them, stricter enforcement of illegal immigration is much more justifiable.
All this system requires is that the federal government maintains and checks on a list of expanded green card holders (ie non-citizens) that are restricted to certain states. This system is already in place for normal green card holders. If you aren't where you're supposed to be, the feds start looking with you, with the added advantage of having a last known location, picture, description, identifiers, and information about your family and friends. It would be much easier to track people who entered legally, and justifies much stronger controls over illegal entry.
Hypothetical situation: California says "okay we'll take 30,000 Syrian refugees annually". The Feds screen, admit, and register 30,000 Syrians and tell them "Okay, you are not citizens- you can't leave California without a visa, you can't vote, and you might never become citizens. You may live and work in California as long as you pay state and federal taxes, and you can use public education and medicaid (after ten years). You will be tried for a felony if you leave California. We will check with your landlord, check on where you pay taxes, and stop by every 3-6 months to verify where you are". In return the refugees provide everything a normal green card holder does- name, identification, family, location, occupation etc.
Edit: the best argument I've heard against this is the deontological one. Essentially that the feds should be the only ones who control who enters the union, and that since they are the feds they can't contain people in one state. This argument completely disregards the possibility of the feds making deals with states.