It isn't that simple.
It seems reasonably clear that the president can't withhold Federal funds without Congressional authorization. But can Congress do that? That's a more nuanced question.
It is a long-standing rule that Congress can put constraints on funds that it provides to the States under the Spending Clause. For example, Congress can say it will help fund schools, so long as the State runs the schools in ways Congress requires. The Court characterizes this as a permissible "condition" of the Federal funding. But it is equally clear that Congress cannot impose conditions that are not connected to the funding. The Court calls this impermissible "coercion" in contrast to a permissible "condition".
Remember back to the Obamacare provision that penalized states that refused to expanded Medicare by stripping them of all Medicare funding. The issue was whether this was a constitutionally permissible "condition" or constitutionally forbidden "coercion". Congress/Obama argued that it was a condition because they were withholding Medicare funds based on a State's refusal to expand Medicare. The challengers argued that this was not a close enough nexus. They said that the purpose of the existing Federal funding was to provide coverage for disabled people, single parents, deeply impoverished parents, etc. The ACA tried to expand coverage to all people (parents or not) who earn up to 125% of the poverty levels. The issue boiled down to whether this was enough of a nexus.
In the opinion (
link), the Supreme Court interpreted the germaneness requirement very narrowly. The opinion is a jumbled mess of concurrences and dissents, but all of the relevant discussions are clustered under Part IV of each opinion. Chief Justice Roberts wrote the Court's opinion, in which Justices Breyer and Kagan joined. Justices Scalia, Kennedy, Thomas, and Alito issued decisions that dissented from the Court's judgment, but concurred in the analysis of this particular issue. All told, that's 4 conservative votes, 1 centrist vote, and 2 liberal votes for the idea that not even Congress can withhold Federal funds for reasons that aren't closely and logically related to what the funds being withheld were granted for in the first place.
So, to enforce a requirement that the State use its own resources to help the Federal government enforce Federal deportation laws, Congress can restrict germane funding. If the Court is intellectually honest, this would not include all funding, or even all funding related to law enforcement. At a minimum, it would have to be funding related to immigration enforcement, and would probably have to be limited more narrowly to funding related to deportation. I don't think there is any such funding, and if there is it isn't much.
Could individual justices abandon principle and flip flop sides to get the result they want, logic be damned? Of course they could. And I would predict that Thomas, Alito, Sotomayor, and Ginsberg would do just that. Thomas and Alito would basically be saying "Obama can't do it, but Trump can" and Sotomayor and Ginsberg would basically be saying the opposite. Those flip flops would be a wash, with the same 2-2 result in both cases.
It is clear that Breyer and Kagan would vote their conscience, having established their intellectual honesty by voting to strike down the ACA provision. There is zero doubt that they would also strike down any Trump overreach. That's 4 votes.
Thus, the question is what Chief Justice Roberts and Justice Kennedy would do. I find them both to be intellectually honest, resolving most cases on their merits instead of basing their opinions on political outcomes. Thus, I think it is likely that any overreach by Trump on this issue would be stricken down 6-2.
For what it's worth -- this is an inherently conservative position, with which I very much agree. Enforcement of Federal law is a Federal issue that should be accomplished by Federal agents using Federal funds. The Federal government should not have the authority to coerce States to cooperate. Anyone who thought Obamacare was an overreach but supports Trump on this issue is a hypocrite.
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