Under the complex funding formula in the agreement, the Department of Homeland Security would have “reprogramming authority” to transfer as much as $750 million from other programs into detention.

“In short, there is more than enough flexibility for ICE to respond to any forthcoming surges in illegal immigrations and apprehensions,” the document said.

Two Democratic aides said the Republican memo was accurate in theory, but added that such a drastic expansion in beds was unlikely because it would require taking money from other important programs, such as disaster relief.

Democrats on the committee that hashed out the deal, under pressure from immigrant rights groups and their party’s ascendant liberal wing, stalled talks over the weekend by demanding that any deal include a cap of 16,500 beds dedicated to housing detainees apprehended through sweeps of communities away from the border. There are currently 20,000 such slots.

Immigrant rights advocates expressed disappointment. “For the last two years, we’ve been in a defensive posture, working to hold the line and prevent the bad, but now House Democrats have the power to start doing good,” said Lorella Praeli of the American Civil Liberties Union, which has sued the Trump administration over its detention policies.

On the other side of the ideological divide, Representative Tom Graves, Republican of Georgia and one of the 17 House and Senate lawmakers negotiating a deal, said on Twitter that he had not signed off or seen a final agreement. But “based on the reports, I have concerns,” he said. “Lots of questions too.”

Senator Richard C. Shelby, Republican of Alabama, the chairman of the Senate Appropriations Committee and one of four lawmakers who worked out the accord, said he was not worried about objections from the right.

“In some areas, we probably got more than a lot of people expected, and in some areas we didn’t get as much,” he said. “But that’s the nature of the beast.”