“Having this all out in the public open like this is not ideal if your goal is to apprehend people and detain them,” said Ms. Brown, the director of immigration policy at the Bipartisan Policy Center. “If your goal is to put fear in people and make them afraid, mission accomplished.”

While President Trump said on Twitter this week that ICE would deport millions of undocumented immigrants, the acting secretary of homeland security, Kevin McAleenan, is said to have resisted the operation because of the logistics behind it. That reluctance has been met with displeasure at the White House.

The agency does not have the resources to carry out a mission of that size, and its deportation officers, which number about 6,000, also do not know the addresses of many of the undocumented immigrants.

Some immigration experts doubted that the agency would reach the target of 2,000, partly because families most likely fled their homes after Mr. Trump’s tweet late Monday night. “They know we’re coming,” said Ronald D. Vitiello, the former acting director of ICE.

In advance of the effort, agents from Homeland Security Investigations, who usually conduct long-term investigations rather than deportations, have been directed to join deportation officers.

Homeland security officials have been wary of the coordinated effort because it could lead to the separation of families. It is unclear what will happen if ICE agents encounter undocumented parents at home while their children, who may be citizens, are away.

“Past raids have left children alone and afraid in empty homes, praying they won’t be left to care for younger siblings by themselves, with no idea if they’ll see their parents again,” said Sandra Cordero, the director of Families Belong Together, an advocacy group.