The developments all come as Obama has declared comprehensive immigration legislation dead in Congress and announced plans to proceed on his own by executive action to make whatever fixes he can to the nation's dysfunctional immigration system.
That could put Obama in the seemingly contradictory position of weighing proposals to shield millions of people from deportation while at the same time trying to hurry deportations for the unaccompanied children.
Congressional Republicans blame Obama policies for the confusion; Obama administration officials dispute that.
More than 50,000 children have arrived since October, in many cases fleeing violence at home but also drawn by rumors that they can stay in the U.S.
Obama plans to discuss the crisis with faith and local leaders during a political fundraising visit to Texas on Wednesday, but he is resisting calls to visit the border for a firsthand look. The White House invited Texas Republican Gov. Rick Perry, who is among those urging Obama to get to the border while he's in the state, to Wednesday's meeting in Dallas.
Perry's spokeswoman Lucy Nashed confirmed that the governor and Obama would meet.
Perry "is pleased that President Obama has accepted his invitation to discuss the humanitarian and national security crisis along our southern border," Nashed said.
House Appropriations Committee Chairman Hal Rogers, a Republican, called the situation on the border "extremely dire."
"It is clear that additional funding will be needed to ensure the proper care of these unaccompanied children, to enforce the law, and to further secure our border so that these problems can be mitigated in the short term," he said in a statement. "Our committee will focus on providing what is necessary to meet these ongoing needs."
The White House request would:
• Seek $1.1 billion for the Department of Homeland Security to help deter border-crossers and increase enforcement. That would include $879 million to pay for detention and removal of adults traveling with children, to provide additional detention space for those individuals, and to speed up the prosecution of adults who cross the border unlawfully with children;
• Seek $433 million for Customs and Border Protection to cover overtime costs and for additional facilities to detain unaccompanied children while they are in Border Patrol custody. It also includes nearly $40 million to increase air surveillance, such as drone flights along the border;
• Provide $64 million to the Department of Justice, with much of the money spend on hiring 40 additional teams of immigration judges. The White House says that together with a previous request for 35 additional teams, the system would be able to process an additional 55,000 to 75,000 cases annually;
• Provide $1.8 billion to the Department of Health and Human Services for the care of unaccompanied children, including shelter and medical care.
As lawmakers return to Washington this week from a weeklong recess, Obama's spending request is set to be a focus, with the Senate Appropriations Committee scheduling a hearing to examine it.