There are USSC rulings that make it difficult to coerce the states by threatening their current funding. I am not a lawyer and I may be wrong about where the legal boundaries lie, but the main legal way Congress can act is on issues involving future funding. For example if Congress wanted to encourage voter reform and provided say $100 Billion to cover the cost, then they could set conditions to qualify. But they generally cannot say “if you don’t detain suspects for ICE we will cut off funding for XYZ”
Unless of course, the funds already had set conditions. Then if a state refuses to abide they can lose funding.
Another way they may be able do it is to change the law as it applies to all states.. This may be politically acceptable, too, since the states that voted for Hillary are the ones with the majority of immigration. So such a move may work since the GOP may not get much political blowback. Just speaking in general terms for illustration, Congress could repeal programs for social welfare and replace them with new programs that are contngent on certain conditions. If they tried this, it will be one heck of a fight with tons of protest.
If you can read simple English it is enough to figure out when this law is being broken.
Federal Immigration and Nationality Act
Section 8 USC 1324(a)(1)(A)(iv)(b)(iii)“Any person who . . . encourages or induces an alien to . . . reside . . . knowing or in reckless disregard of the fact that such . . . residence is . . . in violation of law, shall be punished as provided . . . for each alien in respect to whom such a violation occurs . . . fined under title 18 . . . imprisoned not more than 5 years, or both.”
Section 274 felonies under the federal Immigration and Nationality Act, INA 274A(a)(1)(A):
A person (including a group of persons, business, organization, or local government) commits a federal felony when she or he:
• assists an alien s/he should reasonably know is illegally in the U.S. or who lacks employment authorization, by transporting, sheltering, or assisting him or her to obtain employment, or
• encourages that alien to remain in the U.S. by referring him or her to an employer or by acting as employer or agent for an employer in any way, or
•knowingly assists illegal aliens due to personal convictions.
Penalties upon conviction include criminal fines, imprisonment, and forfeiture of vehicles and real property used to commit the crime. Anyone employing or contracting with an illegal alien without verifying his or her work authorization status is guilty of a misdemeanor. Aliens and employers violating immigration laws are subject to arrest, detention, and seizure of their vehicles or property. In addition, individuals or entities who engage in racketeering enterprises that commit (or conspire to commit) immigration-related felonies are subject to private civil suits for treble damages and injunctive relief.