(CNN) President-elect Donald Trump will face several significant hurdles if he attempts to quickly make good on a campaign promise to deport millions of undocumented immigrants from the United States, according to multiple immigration experts and law enforcement officials interviewed by CNN.

The likely obstacles to any mass deportation effort include required congressional approval for increased spending, vows of resistance by leaders in several major cities that are home to large numbers of potential deportees and long waits for removal proceedings in US immigration court.

"He's hamstrung," said Muzaffar Chishti of the Migration Policy Institute, a non-partisan Washington-based think tank. "He did not understand that we don't have a monarchy. We did not elect King Trump."

As Trump's inauguration approaches, there has been widespread handwringing among undocumented immigrants and their advocates as they wait to see how US immigration policy may change under a Trump administration. But there is mounting evidence that whatever actions he takes will not match the harsh rhetoric of the campaign trail.

He's already waffled on his promise to build a wall, saying that existing fencing may suffice in some sections of the border. His controversial pledge of a temporary ban on all Muslims entering the US seems all but forgotten.

That leaves the deportation pledge.

"Mr. Trump will not be able or willing to engage in the kind of mass deportations that he promised in his campaign," said Stephen Legomsky, a professor emeritus at Washington University School of Law in St. Louis.

'More difficult than it sounds'

"Simply finding large numbers of undocumented immigrants with criminal records is much more difficult than it sounds," said Legomsky, who served as former chief counsel to US Citizenship and Immigration Services from 2011 to 2013 and as a senior counselor to Homeland Security Secretary Jeh Johnson in 2015.

Legomsky, who has since left government, said any such effort would be "incredibly laborious" and cost prohibitive.

Early in the presidential campaign, Trump said all 11 million illegal immigrants in the US should be deported. He seemed to soften his stance after the election, telling CBS' "60 Minutes" that he would prioritize going after undocumented immigrants who had committed crimes beyond being in the country illegally.

The irony of that approach, experts say, is that it would be much easier for Trump to locate and begin deportation proceedings of non-criminals such as those granted temporary amnesty under President Barack Obama's Deferred Action For Childhood Arrivals Program.

The program, known as DACA, granted some 840,000 childhood-arrivals to the US temporary protection from deportation and issued them work permits. It was created by executive memorandum in 2012 and could be immediately rescinded by the Trump administration, stripping DACA participants of their protection against deportation.

Going after undocumented immigrants with criminal records could prove more difficult and would likely require congressional approval to pay for more Immigration and Customs Enforcement agents to round up potential deportees who do not want to be found.

Key to that effort would be the cooperation of local law enforcement who run county jails and have the ability to alert ICE agents to the presence of undocumented immigrants with criminal records in their custody. Such inmates can be placed on an ICE "detainer" indicating that they are to be handed over to immigration officials when they finish their sentences. This could provide a steady flow of potential deportees without having to conduct costly and time-consuming searches.

But many big cities with large undocumented immigrant populations have said they would refuse to cooperate with such deportations under most circumstances. Some cities, including Los Angeles and Chicago, have set up legal defense funds for undocumented immigrants facing deportation.

Trump's threat

Trump has threatened to withhold federal funding from cities that don't cooperate with US immigration efforts -- an approach that could cripple local schools, police departments and airports, among others.

But Chishti predicted any such effort would face an immediate legal challenge. He said there were several Supreme Court cases that stood for the proposition that the federal government can't indiscriminately "hold a gun to the states' head."

A threat to withhold funds, he said, "must be in relation to the dispute at hand."

Even if officials were able to initiate a surge in deportation cases, such an effort would likely stall in immigration court where there is currently a backlog of more than a half million cases and a wait time of nearly two years.

Mark Krikorian, executive director of the Center For Immigration Studies, a non-partisan think tank in Washington, said Trump's campaign pledges to deport millions amounted to an "Archie Bunker moment" that should not have been taken seriously.

"He's not going to be snapping his fingers and deporting millions of people over night," said Krikorain, whose group's motto is "Low-Immigration, pro-immigrant."

"That's not realistic," Krikorian said. "No one thinks that's going to happen."

But Krikorian said "it's very plausible" that Trump could ramp up deportations by 25% or more in 2017 and return to levels seen under Presidents Bill Clinton and George W. Bush, which he said reached about 400,000 a year when Bush left office.

That, he said, could be done without significant budgetary increases and despite resistance from sanctuary cities.

"I think the other side is making it seem more complicated than it needs to be," he said.

Stephen Yale-Loehr, who teaches immigration law at Cornell Law School, agreed that Trump would be able to have meaningful impact during the first year of his presidency, but not to the extent suggested during the campaign.

"On the campaign trail things are not nuanced. They're black and white," Yale-Loehr said. "It takes a while to turn the battleship of bureaucracy around."