Congress' limited power over immigration is its power of taxation!
Congress does not have authority to assume powers not authorized by our Constitution.
Under what provision of our Constitution has Congress authority to admit tens of thousands of immigrants into the United States and compel the States to accept them?
The only power I see in the Constitution relating to this issue is that which is found under Article 1, Section 9, and allows a tax or duty to be imposed on the importation of foreigners, but leaves the State free to admit whom they please.
"The Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a Tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person."
JWK
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States, respectively, or to the people.___ Tenth Amendment