When it comes to immigration policy, the best-known clash between federal and lower levels of government is the recent battle over Arizona's infamous SB 1070, a law that intensified the border clampdown. And there have been plenty of other times a state or city has tried to be more heavy-handed in its immigration enforcement than the feds. But sometimes it's the more local jurisdiction that's less eager to crack down, as Emily Badger points out in The Washington Post:
One by one, these cities—soon to be joined by New York City—have passed resolutions or enacted new policies refusing to hand over immigrants detained by local police to federal officials for deportation. The strategy, gaining further momentum this year with a statewide law in Colorado, is one way local governments dismayed by a broken federal immigration system have found to undermine it.
At issue are what are called "immigration detainers." The federal government relies on local law enforcement agencies to help identify individuals for deportation. When local police come in contact with suspected immigrants (for reasons ranging from serious offenses to traffic violations), Immigration and Customs Enforcement often issue a detainer, asking local jails and prisons to hold them for 48 hours or more beyond their release to give the feds time to decide if they want to collect and deport them.
Badger mentions civil libertarian objections to the imprisonments, and she also notes fears that these detentions will undermine other sorts of police work. (People tend to be less likely to help a homicide investigation if they're afraid they'll be hauled in on immigration charges.) But the most important incentive that she identifies might be the financial one: "The federal government doesn't reimburse local agencies for resources they spend 'holding' suspected immigrants on ICE's behalf." Just as governors with no ideological objection to regulation can suddenly sound like fire-breathing libertarians when confronted with an unfunded mandate, ICE's orders can turn a moderate's thoughts toward defiance.
Bonus link: An earlier example of immigration-friendly federalism.