Mr. Shanahan lobbied lawmakers to approve the disaster aid package, citing a number of military bases damaged by hurricanes last year. Mr. Trump spent time on Wednesday visiting Tyndall Air Force Base in northern Florida, which is still recovering from Hurricane Michael, but did not address the debate over disaster aid.
House Democrats are still examining the request for more border funding, which would provide money for both humanitarian necessities and more beds to hold migrants in custody, according to an aide.
But immigration officials, in separate testimony before the Senate Judiciary Committee, argued that congressional action was needed to counter what Carla L. Provost, the chief of the Border Patrol, called “off the charts” numbers of people detained.
In April, immigration officials said, 109,144 migrants were detained crossing the border without permission, bringing the total number of unauthorized crossings this year to 460,294. More than half of the monthly arrests were people in families.
“It’s like holding a bucket under a faucet,” Ms. Provost said. “It doesn’t matter how many buckets you give me if we can’t turn off the flow.”
“Our nation cannot solve today’s crisis with yesterday’s framework,” she added.
Like other immigration officials pressed on the administration’s budgetary requests in recent weeks, Ms. Provost and other officials described an overwhelmed immigration system, short-staffed and unprepared to deal with not only a high number of migrants, but also young children and families at facilities intended for single adults.
“I don’t really care how you label it,” Senator John Cornyn, Republican of Texas, said at the hearing. “The entire system is breaking, and it’s unsustainable.”
Democratic lawmakers on the committee focused on the Trump administration’s policies, which Senator Richard J. Durbin of Illinois said “made our border less secure and many times undermined our American values.”