WASHINGTON — Denver and Aurora stand to lose millions of dollars in federal funds if Donald Trump carries out a pledge to isolate so-called “sanctuary” cities that do not compel their police officers to enforce immigration laws.

Trump campaigned on a platform that included a vow to “cancel all federal funding to sanctuary cities,” and his Nov. 8 victory has prompted a mix of soul-searching and defiance among many of the nation’s municipal leaders.

The mayors of Chicago and New York said they wouldn’t change city policies that limit cooperation with immigration officials; Denver Mayor Michael Hancock echoed that position in an interview Wednesday.

“We are not going to do the job of the federal government. What we are going to do is make sure we remain an inclusive city,” said Hancock, who added it still was “too early” to assess the likelihood of Denver losing federal funding.

Taken to the extreme, Trump’s policy would have a major impact on Denver. The city received more than $175 million from federal sources in 2015 — a big chunk of the city’s total annual budget of about $1.9 billion. Aurora received about $11.5 million in federal funds out of its 2015 budget of roughly $627 million.

But how — and if — Trump enforces this policy is a big question.

There is no standard definition of what constitutes a sanctuary city. In Aurora and Denver, there are no ordinances that specifically prohibit police officers or other city officials from helping federal authorities enforce immigration law.

Law enforcement officials in those two cities, however, said this week they would continue the practice of leaving immigration enforcement to federal agents. Oftentimes this means complying with requests to detain suspects who are believed to have violated U.S. immigration law; a policy that has been challenged in court.

“Officers will not enforce, investigate or detain individuals based on their immigration status,” wrote Aurora Police Chief Nick Metz in a Facebook post. “It is our goal to ensure that all individuals within Aurora feel safe in reporting emergencies and working closely with the APD to ensure our city remains a safe place for all.”

Whether this fits Trump’s definition of a sanctuary city is an open question — as is the level to which Trump would press to cancel federal funds — though the president-elect was adamant about his intention during a speech in September.

“Cities that refuse to cooperate with federal authorities will not receive taxpayer dollars, and we will work with Congress to pass legislation to protect those jurisdictions that do assist federal authorities,” he said.

Congress has tried before to penalize cities that do not play ball; last year, Democrats blocked legislation by Sen. David Vitter, R-La., that would have cut some — but not all — federal funding, such as community development grants and money for the Community Oriented Policing Services Program, or COPS.

Once in office, Trump likely would need the support of Congress to put his pledge into action, a challenge given that Republicans do not hold a filibuster-proof majority in the Senate, though the GOP will control the House, Senate and White House.

In Colorado, Trump’s policy has at least one supporter: U.S. Rep. Mike Coffman, R-Aurora, who represents a suburban Denver district that has large Latino and immigrant populations.

After disowning Trump during the campaign — and touting his own shift on immigration issues — Coffman this week expressed enthusiasm in working with the president-elect and voiced support for Trump’s pledge to target cities such as Aurora.

“I’ve voted in the past to withhold federal funding for sanctuary cities and I will continue to do so,” Coffman said in a statement.

That’s in contrast with Democratic U.S. Sen. Michael Bennet of Colorado.

“Michael opposes efforts to withhold funding to local governments as a means of coercing them to enforce federal immigration laws,” said Laurie Cipriano, a Bennet spokeswoman, in a statement.

A new study by the Pew Research Center estimated that in 2014 there were 11.1 million immigrants living illegally in the U.S. — a figure that’s held steady since 2009. About 200,000 of those residents lived in Colorado.

In Boulder, Trump’s threat to starve cities that do not help immigration officials appears to have triggered the opposite reaction — the city council this week asked staff to investigate the ramifications of declaring Boulder a sanctuary city.

“While we have no idea what this new administration will do, we thought we should become better informed about our options so that we can effectively defend the civil rights of all our residents regardless of their immigration status,” wrote Mayor Suzanne Jones in an e-mail.