President-elect Donald Trump swept to the White House promising to clamp down on illegal immigration and so-called "sanctuary cities" like Minneapolis and St. Paul whose leaders vow not to act as local immigration enforcers.

Republicans around the country — including the newly empowered GOP majorities in the Minnesota Legislature — have followed suit, threatening to withhold government aid from cities that decline to work with federal immigration authorities and represent themselves as safe havens against deportation.

"Cities don't get to choose a cafeteria-style selection of laws that they will enforce and they won't enforce," said Sen. David Osmek, R-Mound, who sits on the Local Government Committee.

"If they don't want to follow the laws, then I don't think they should get the taxpayers' money," he said.

Statements like these have some local government officials on edge. They're wedged between increasingly diverse, liberal-leaning constituents opposed to hard-line immigration rhetoric from Trump and other Republicans and the tough decisions that would follow losing scarce state and federal dollars for policing and other local services.

After Trump won the election, Minneapolis Mayor Betsy Hodges released a statement affirming the city's policy on immigration: "I will continue to stand by and fight for immigrants in Minneapolis regardless of President-elect Trump's threats," she said.

The sharp, clear rhetoric on both sides masks a more complex reality: The term "sanctuary city" has no legal meaning. And both advocates and opponents of stricter immigration enforcement agree that undocumented immigrants in cities like Minneapolis and St. Paul should realize the cities' ordinances don't actually provide much sanctuary.

Regardless, cities and immigrant rights groups are steeling themselves for a crackdown.

More than a decade ago, both Minneapolis and St. Paul enacted "separation ordinances," which means city employees — including police — do not ask about immigration status. City leaders argue the ordinances encourage crime victims and witnesses to come forward regardless of immigration status.

"St. Paul's separation ordinance does not defy immigration law, but simply emphasizes the separate role of local law enforcement from federal immigration enforcement," St. Paul Mayor Chris Coleman said in a statement to the Star Tribune. "While they may assist federal officers in the investigation of criminal activity involving someone who may also be violating federal civil immigration laws, our police officers are not [ICE] agents," he said, referring to U.S. Immigration and Customs Enforcement.

That classifies Minneapolis and St. Paul as "don't ask" cities, said Virgil Wiebe, professor at the University of St. Thomas School of Law. This is distinct from and milder than "don't tell" jurisdictions like San Francisco, which limits employees from working with federal immigration officials.

For anyone arrested, however, there's no sanctuary from federal immigration enforcement.

A suspect arrested in Minneapolis, for instance, is brought to Hennepin County jail. He or she is photographed, fingerprinted and questioned about immigration status. Biometric information is sent to a state repository, which then goes on to the FBI, which forwards relevant data to the Department of Homeland Security, making its way back to the local ICE office within 30 minutes, said Hennepin County Sheriff Rich Stanek. He runs the county jail, which books 40,000 inmates from all over the county every year.

"It's just rhetoric," Stanek said of cities' declaring themselves sanctuaries.

Still, Stanek caught the attention of immigration hard-liners after a 2014 decision by the sheriff and other local officials to release inmates after they have been adjudicated, rather than holding them at the request of ICE.

Stanek and sheriffs around the country faced potential litigation because, by holding the detainees without a warrant, authorities were violating Fourth Amendment rights, lawyers for detainees argued.

Wiebe, the St. Thomas law professor who has represented detainees around the state, endorsed the move: "Rather than call Hennepin County a sanctuary county, it's a Fourth Amendment county," he said.

Stanek said he still holds detainees if ordered to by a judge or as emergency circumstances require.

Rep. Duane Quam, R-Byron, has already introduced a bill that would force local officials to hold detainees at the request of ICE.

Trump, Congress and the Legislature could also try to force cities to use their police departments to enforce immigration law, using the threat of lost funding as leverage.

Minneapolis is set to receive nearly $78 million in local government aid from the Legislature in 2017, while St. Paul will receive $62 million, according to Minnesota Management and Budget.

Rep. Steve Drazkowski, R-Mazeppa, who chairs a property tax committee that has jurisdiction over local government aid, said the committee would take a hard look at local aid, targeting both wasteful spending and local officials "breaking or ignoring federal law."

North Carolina passed a law in 2015 that sought to clamp down on sanctuary cities. Former Republican Gov. Tim Pawlenty attempted similar measures during his tenure but lacked support from the Legislature.

One thing is certain: If and when Republican lawmakers wade into immigration politics, they'll get a fight.

"The Bible is clear," said JaNae Bates, spokeswoman for progressive faith-based group ISAIAH and a United Church of Christ minister.

"We are to be welcoming, open to the stranger, and we stand with city and county leaders and will do what we can to protect everyone in our community, including citizens and immigrants — documented and undocumented alike," she said.

Adam Belz contributed to this report.