"It's our view that it's unlikely that most of these kids will qualify for humanitarian relief. If they don't qualify for humanitarian relief," Earnest said, "they will be sent back."
Earnest's pointed response comes a day after Homeland Security Secretary Jeh Johnson danced around questions over whether the children would be allowed to stay in the United States.
"There is a deportation proceeding that is commenced against illegal migrants, including children," Johnson said Sunday on NBC's "Meet the Press." "We are looking at ways to create additional options for dealing with the children in particular, consistent with our laws and our values."
The White House will formally ask Congress Tuesday for $2 billion in emergency relief to help stem the tide. The White House said it wants, among other things, to place additional immigration judges on the border to help expedite cases.
More than 52,000 unaccompanied children and 39,000 women with children have been apprehended at the border this year, a surge that seems to have caught the administration off guard. Last month Obama directed federal agencies to coordinate a response to provide housing and other services to the children, who are currently being held in California, Texas, Oklahoma and other places while awaiting processing.
Earnest said the Department of Homeland Security will seek from Congress "additional authority" to deal with the issue "in a humanitarian way, in a way that's in line with our laws."
Earnest said the administration wants to ask Congress for Johnson to be able to "exercise discretion to more promptly remove children" from the United States.
President Obama will travel to Texas this week to attend fundraisers and deliver remarks on the economy in Austin. He will not visit the border. Earnest said the administration is "not worried about those optics" of the president fundraising while what the administration has called an "urgent humanitarian situation" is happening hundreds of miles away.
Earnest said a number of administration and White House officials have traveled to the border, and Obama is "very aware of the situation that exists on the southwest border," Earnest said.