Eggelston's meeting with members of the Congressional Hispanic Caucus in House Minority Leader Nancy Pelosi's
office was intended to convince House Democrats to hold off sending a letter to Obama urging him to stop the raids, according to multiple House Democratic sources familiar with the discussions.
Senate Minority Leader Harry Reid
, meanwhile, said he spoke with Homeland Security Secretary Jeh Johnson.
"I spoke to the secretary of Homeland Security at 12:30 today and he understands the concerns we have," Reid told reporters. "I think we're moving forward to a resolution to this. I think you're going to find a pause in these deportations."
Reid's communications director, Kristen Orthman, says his comments were "reflecting his hope there will be a pause" as opposed to his knowledge that a pause is likely.
House letter to Obama
Illinois Democratic Rep. Luis Gutierrez stressed this is one issue where congressional Democrats, as well as the three Democrats running for president in 2016, have been unified.
"They may not agree who's good on guns or income equality, but they are all fighting for the immigrants," Gutierrez said about Hillary Clinton, Bernie Sanders and Martin O'Malley.
Rep. Zoe Lofgren called the meeting with Eggleston, which was first reported
by Politico, "cordial," but the discussion with Eggleston didn't satisfy the concerns of those who attended and a group of House Democrats held a press conference to release the letter.
Lofgren and Gutierrez told reporters that they were not informed of any potential pause by anyone from Eggleston in their meeting Tuesday, or by anyone in the administration.
"A pause is important because it sends a message to the community that you know what -- when you raise your voice that somebody listens," Gutierrez noted.
Lofgren said the U.S. deports 700 to 1,000 people every day, but "for women who children who fled three countries because of violence we want to make sure they had an adequate chance to present their situation."
So far, 146 House Democrats have signed the letter to Obama.
House Democrats had delayed the press conference as a courtesy to the White House, according to sources.
The letter maintains that the Obama administration supports those fleeing violence in the Middle East, Africa, and Asia, but has not applied this approach to those from Guatemala, Honduras, and El Salvador.
"The brutality of violence in Central America is undeniable, and yet this administration has failed to provide a comprehensive refugee solution for those seeking international refugee protection," the letter states.
The members raised concerns that the Department of Homeland Security "may have already removed mothers and children from the United States and returned them to violent and dangerous situations in their home countries."