CHICAGO (CBS) — We don’t know where or when, but President Donald Trump said he plans to move forward with mass deportation roundups “fairly soon,” more than two weeks after postponing a wave of roundups of undocumented families.

Some undocumented immigrants who fear being caught up in raids by U.S. Immigration and Customs Enforcement have taken sanctuary at churches in Chicago, including Lincoln United Methodist Church in Pilsen.

The church braced for possible ICE raids two weeks ago, before the president delayed the mass deportations. At the time, Trump threatened to order the ICE raids unless Democrats agreed to revise the nation’s asylum laws within two weeks.

Efforts to reform the U.S. immigration system have failed under both Republican and Democratic administrations, and there is currently no legislation with sufficient bipartisan support to pass in both chambers of Congress, especially during the timeline the president has demanded.

On Friday, the president said the roundups would be “starting fairly soon.”

Meantime, community activists and immigration attorneys have been going out into neighborhoods across Chicago to educate undocumented immigrants about their legal rights. Some of the advice they’ve been giving has been to remain silent until lawyers are present, and not to sign any documents they don’t understand.

“Those undocumented workers that have a criminal background, that’s who their high priority has been. So that’s who their high priority has always been,” immigration attorney Jorge Montes said. “That would be probably the first group that they’re after and that should be leery of what is going to happen.”

Montes said undocumented immigrants also should know they should not open the door of their home to anyone without knowing who it is. If it turns out ICE or Homeland Security agents are knocking on their door, they should demand to see a warrant before letting agents in.

Mayor Lori Lightfoot has said she instructed Chicago police that the department cannot, in any way, facilitate any ICE raids.

The president’s supporters have said he’s honoring campaign promises, and enforcing laws that have been ignored too long.

Under the operation — which ICE said would send a “powerful message” of deterrence to would-be migrants in Central America considering journeying towards the U.S.-Mexico border — authorities had been expected to carry out a series of raids in major U.S. cities to apprehend and deport families who received an order of removal from a judge.

Last month, the president claimed that “millions” would be deported under a new wave of operations — something likely to be logistically impossible given the resources and manpower ICE has at its disposal. Last year, ICE removed more than 250,000 people. The highest number of yearly deportations came during the Obama administration in 2012, when the agency removed approximately 410,000 undocumented immigrants.

Any large-scale deportation blitz would also likely spark a massive public outcry and affect not only undocumented immigrants with pending removal orders, but millions of mixed-status families with members who are U.S. citizens.

Acting U.S. Citizenship and Immigration Services Director Ken Cuccinelli, who as the Virginia attorney general and a Republican state lawmaker pushed several anti-immigration positions, said ICE’s efforts to remove undocumented immigrants have been “held up” and “interfered” with by the politics in Washington. He suggested that people should not be surprised about officials carrying out these operations.

“Here we are talking about ICE doing its job as if it’s special, and really this should be going on a rolling basis,” he said, adding later, “They’re looking forward to just doing their jobs.”