President Donald Trump this week announced ambitious plans to step up immigration enforcement and arrest and deport undocumented people at a record pace. He’s not going to get a lot of help in Illinois.

Despite the prospect of losing federal funding for resisting Trump’s efforts — a threat being explored by the administration — Cook County Sheriff Tom Dart said he had “no interest” in devoting his deputies’ time to arresting undocumented county residents, and Mayor Rahm Emanuel has consistently said Chicago will remain a “sanctuary city.”

On Thursday, state Attorney General Lisa Madigan said her office is looking into ways to offer legal backup to smaller towns that want to continue their resistance to immigration laws. Gov. Bruce Rauner, in response to an open letter from Madigan earlier this month, said he had no plans to deputize the Illinois State Police to enforce immigration laws.

“The only way for them to do a lot of what they’ve pledged to do . . . is work with governors, work with states, to get state and local law enforcement to enforce immigration laws,” she said Thursday. “We don’t have enough resources to combat the violent crime we have. To redirect law enforcement to do federal immigration work only further dissipates the resources we have to deal with the violent crime problem.”

So-called sanctuary cities have for years declined to cooperate with federal immigration officials, a stance that mainly means law enforcement won’t ask questions about people’s immigration status, won’t share information about the topic with federal agencies, and won’t hold arrestees solely based on violations of federal immigration law without another criminal warrant.

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The sheriff’s department won’t honor Immigration and Customs Enforcement “detainer” requests, which would require the jail to hold arrestees flagged with immigration law violations for up to 48 hours, but the jail will hold offenders on a criminal warrant from ICE, according to a 2011 county ordinance.

Spokeswoman Cara Smith said the jail gets only a few such requests each week. She said the department was still calculating the amount of funding the jail receives from federal programs.

From January 2014 to September 2015, the county declined more than 450 detainer requests, said Jessica Vaughan, policy director of the Center for Immigration Studies, a think tank that backs stricter immigration laws. That total ranked the Cook County Jail No. 9 for the number of potential ICE detainees released during the span, Vaughan said.

Chicago and Cook County are known to be among the least-cooperative law enforcement agencies when dealing with ICE, Vaughan said, citing a 2016 Justice Department report analyzing the issue — a report that also found the DOJ could potentially claw back more than $4 million in funding. The report predates the Trump administration, Vaughan notes.

“Congressmen in the house . . . leaned on DOJ to start enforcing federal law that prohibits the kind of sanctuary policy that Cook County and Chicago have,” she said.

Still, the $4 million is a relative drop in the bucket for Chicago. A Reuters report found that the city received $524 million in federal funds, money that went to everything from the Head Start pre-kindergarten program to revamping L platforms.

“Even if they took every [federal] dollar for law enforcement funding, that’s only about 1 percent of the municipal budget,” said Nadav Shoked, a Northwestern University Law School professor who specializes in municipal law.

Whether the White House will start to close off federal dollars for other programs with less clear links to the city’s immigration stance remains to be seen, Shoked said. He noted that the issue becomes more still murkier if Congress becomes involved. The National Minimum Drinking Age Act in the 1980s threatened to reduce federal highway funds to any state that didn’t set the legal drinking age at 21, Shoked said, and by the 1990s, 21 was the drinking age nationwide.

Shoked said federal agencies could conceivably begin closing off non-immigration enforcement-related funding, even if they were on shaky legal ground in doing so.

“If you look at some of the earlier executive orders, it is clear there wasn’t a lot of legal thinking that went into them,” Shoked said. “Chaos is the order of the day.”

Still, reaction to Trump’s immigration orders from leaders in Chicago and elsewhere seems to indicate they aren’t worried Trump will try to cut large streams of federal revenue.

“It’s not just Chicago, it’s L.A., it’s New York” affirming their status as sanctuary cities, Shoked said. “They don’t seem to think it’s a serious threat, because they’re not doing anything about it.”