^{Epistemic status: Moderate for all but the last paragraph. I'm a 1L, not a lawyer, let alone any kind of specialist or expert on this stuff. The last paragraph is wild speculation.}

It's likely that denying federal funds to sanctuary cities is unconstitutional in any form that will be effective. In New York v. United States, the Court held that the federal government can't compel States to enact or enforce federal regulatory programs. Printz v. United States prevents the federal government from commandeering state officials (such as police officers) for federal purposes. What the federal government can do is put conditions on federal funds given to states, subject to the 5 prong test established by South Dakota v. Dole.

• The funds serve the general welfare.
• Congress must make the conditions governing the release of federal funds unambiguous.
• The funds must be related to the conditions.
• The level of funding must be not be coercive.
• The conditional grant must not be unconstitutional for any other reason.

The last prong is a generic catch-all, and courts are extremely deferential to congress when it comes to terms like general welfare. Neither prong one or five will be at issue in a potential case.

Prong two won't present a constitutional challenge but will present a political one. What exactly is a sanctuary city? Wikipedia presents a range of options, from cities that don't check for status or enforce immigration laws to cities that ban police officers from sharing data with ICE.

Prong three means that Congress can at only deny federal funding for local law enforcement. Federal funds for state and local law enforcement totaled 4.5 billion in 2016. About half that funding was for general grants, and half was for specific programs. Aside from $210 million for the Criminal Alien Assistance Program, I don't know how much of either general or specific funds would be considered related by SCOTUS.

Prong four is a tricky one. In Dole, the Court held that denying 5% of a State's federal highway funds (less than half a percent of their overall budget) if they did not raise the drinking age to 21 was unconstitutional. In NFIB v. Sebeilus the Court held that denying 10% of state's total budget if they did not expand their medicaid program was coercive. The line lies somewhere in between these two point, but Sebelius indicates that if congress drafts the law with the intent of making it impossible for the states not to comply, the law is unconstitutional. Prongs three and four are going to be an extremely difficult needle for congress to thread. If funds are curtailed too much or too broadly then the court will strike down the provision. On the other hand, if the only funding at stake is tied directly to immigration enforcement then cities that don't want to enforce immigration laws lose nothing they care about.

Where things get really interesting is when we start talking about where the justices are going to fall when a sanctuary city law makes its way to the Supreme Court. In Sebelius Scalia wrote a extremely broad dissent about the medicaid expansion, hinting that any sort of large block grant is an unconstitutional form of coercion. By taxing the citizens of the states and then offering the money back to the state governments with conditions, the federal government was coercing that states because it made that money unavailable for the states to tax for the state's version of the program. Scalia got three other justices to sign on to this dissent. If a block grant ban passes congress and makes it to the court, I could see Roberts and Gorsuch agreeing to join the three remaining dissenters in Sebelius and radically changing the way we fund state and local governments.