Herein of Garcia, New York v. United States and Printz, etc

Here is a nice summary from the May & Ides book:

"New York v. United States did not overrule Garcia, for the cases dealt with completely different types of federal action. It is therefore important to understand what Congress can do under Garcia and what it cannot do under New York v. United States. Consistent with Garcia, Congress can, for example, directly regulate the states; as in Garcia, Congress can mandate the wages and hours of state employees. Under New York v. United States, however, Congress cannot use the states as an administrative arm for implementing federal regulatory policy. Thus while the states may be required by Congress to pay their own employees a certain minimum wage under FLSA, the states may not be ordered to have their employees perform certain federally mandated functions such as monitoring private employers' compliance with FLSA. Congress may seek to entice states voluntarily to join a federal regulatory program; they simply cannot be forced to do so. The critical distinction is thus between enticement and direct coercion."

Do you see now why, in Printz, Congress' attempt to commandeer local police departments to perform background checks on purchasers of handguns "does precisely what the Court in New York v. United States says Congress cannot do?" The Brady Act "commandeers states into enforcing a federal regulatory scheme by making local law enforcement officers the administrative agents of the federal government."

If Congress wishes to require background checks on handgun purchasers it must bear the economic and political costs of the program itself, rather than impose them on state officials. When I am upset with federal agents poking their noses into my life and charging excessive fees for the privilege of purchasing a gun, I will know that my beef is with the Federal Government--not state government--and perhaps I will vote accordingly.

Now think about a possible contemporary issue involving sanctuary cities:

Suppose Congress passes a law requiring local police departments to hold illegal immigrants until ICE agents arrive to take them into federal custody.
 

Is this law constitutional?

If not, what could Congress do to get local law enforcement in the states to cooperate with ICE?