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.
You're right that overstays are a big problem. Now imagine how much worse it would be if every state got to choose who comes in. The federal government tries real hard to issue visas only to people who won't break the law. They're not entirely successful, but the bar is decently high.
The Syrian refugee hypothetical would have a different problem altogether. The opposition to admitting refugees isn't economic, it's about terrorism. If you can't stop a terrorist posing as a refugee from traveling from California to Texas then the only way to keep Texas safe from that person is to keep him out of the country altogether.
(To be clear, I think the worry over terrorists posing as refugees is just paranoia. But the fear is real.)
Like I said, the federal government would handle screening. States just admit a number of people, they don't vet them- the fed has primacy there because of national security and immigration control. Regardless you can replace Syrian with Mexican and probably should. I only said Syrian refugees for the sake of variety.
But again, as a national security concern it isn't a problem. As long as the number of state green cards is less than the number of visas granted, a terrorist will be much more likely to get a visa and overstay it if necessary.
How exactly are overstays a problem? It's just a person existing in a geographical area longer than the Mafia controlling it would prefer.
All this "theorycrafting" about how best to coerce people for the greater good is silly.
Blah-de-blah-de-blah the government this and the states that and then "we" make everyone do X and Y because Z and then there will be much rejoicing because people have been successfully coerced for the greater good!
Like if I show up at your door each day and force you to skip on one foot for 5 minutes, at gunpoint, that's good because you might not get enough exercise otherwise!
Anyone can see that would be crazy, but when you talk about some huge, gray abstract masses of people, then it's just fine to intervene in their lives in countless different ways.
How about "we" protect people from becoming drug addicts through a certain harmless "gateway drug" by threatening them with life-ruining prison sentences for using/possessing said gateway drug?
Oh wait, "we" tried that already. It didn't "work"[1], and actually WE had no say in any of it!
[1] Unless, of course, the real goal was to hand everyone else's money to the prison industrial complex, in which case it worked splendidly!
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.