Lose.
The ability to regulate commerce with foreign nations gives the federal government alone the authority to set immigration rules. Controlling the entry through the boundaries of a nation is a natural authority of government. In the case of the US, the only question is "Which government?" The Supreme Court answered this question, "The federal government." For many years, the federal government did not exercise much control in this regard. That does not mean that the authority did not pre-exist the Constitution, belonging to the States, and was not ceded to the federal government.
http://supreme.justia.com/us/92/259/case.html
Fail.
This analysis fails on multiple counts. I will outline them here.
1) Use of the commerce clause to justify unconstitutional actions is (clearly) not a new thing. It doesn't make it right, or just, or otherwise acceptable, but it's certainly been around for a while. It makes no more sense now than it did when this decision was written.
2) This decision predates 14th amendment due process analysis. One right considered fundamental of all people is the freedom to travel. This has been called out and upheld through many different cases. That freedom is not merely called out as "the right of a citizen" to travel, but the right of a person. As each person who attempts to enter the US is under the jurisdiction of our laws, they must go through individual due process before that right can be denied.
3) The analysis of this law does not jive with other decisions, as it makes exercise of a right (freedom of movement, freedom of association) contingent upon payment of a fee. In this case, it goes even further to justify the outright denial of freedom of movement, stating that it is okay for the government to play "onerous, perhaps impossible conditions" upon the exercise of what is recognized elsewhere as a right. You have to choose one, and between further abuse of the commerce clause and denial of freedom of movement and association versus allowing any who would come her to do so, I choose the latter.
4) Other cases which cite this (e.g.
Mountain Timber Co. v. State of WA) point out that the main thrust of this case is "whether a state law deprives a party of rights secured by the Federal Constitution depends not upon how it is characterized, but upon its practical operation and effect."
5) It stretches credulity to suggest the founding fathers would specifically call out naturalization as a power of congress, yet not call out immigration. Having to shoehorn the power of congress into the commerce clause indicates how poor that argument is, when it would stand to reason that an intent to grant the power to limit immigration would have resulted in such being called out as "the power to establish a uniform rule of immigration and naturalization" rather than simply the latter.
We are either a country of enumerated powers, or one where Congress can do anything and justify it because it's "necessary and proper" to protect "commerce". Such a stretch defies logic, and violates the limited government basis of our country.