In private, Republicans responded with a plan that would exempt many detained immigrants from the cap, including those people either charged with or convicted of crimes, including misdemeanor drug offenses and violent felonies. That, in turn, was rejected by Democrats.
“You have ICE agents picking up mothers and fathers and children in their own neighborhoods. That’s why the beds issue is so much more important than the wall,” said Ms. Roybal-Allard, whose Los Angeles-area district is 85 percent Hispanic, the highest percentage of any district in the country.
The number of beds occupied by detainees fluctuates over time, influenced by a variety of factors, including ICE enforcement policies and the flow of migrants at the border with Mexico. The rate of that flow is unpredictable and determined by factors such as the performance of the economies north and south of the border, crime, gang activity and the business practices of coyotes paid to transport migrants from Mexico and Central America to California and the Southwest.
The number of monthly apprehensions of migrants at the border has averaged 25,000 to 40,000 for most of the past decade, but has risen to about 50,000 over the past several months, according to statistics compiled by the Department of Homeland Security.
If ICE does not have enough room to place individuals and family members they detain, they must loosen their enforcement actions, creating a powerful motive for new migrants to enter the country illegally, Trump administration officials say.
“You cannot have border security, without strong interior enforcement, whether there is a wall there or not,” said Matt Albence, the deputy director of ICE, on Monday in a conference call with reporters.
Republicans closed ranks to blast the plan.
“This is a poison pill that no administration, not this one, not the previous one, should ever accept,” Mr. McConnell said on the Senate floor. “Imagine the absurdity of this: House Democrats want to set a limit on how many criminal aliens our government can detain.”