The White House said Monday that most unaccompanied children arriving at the U.S.-Mexico border are unlikely to qualify for humanitarian relief that would prevent them from being sent back from their home countries.

The pointed warning came as the White House finalized a spending request to Congress detailing the additional resources President Barack Obama wants in order to hire more immigration judges and open additional detention facilities to deal with the border crisis. White House officials said they planned to send the more than $2 billion request to lawmakers on Tuesday.

White House spokesman Josh Earnest said that while the administration will allow the immigration review process to take place, officials so far don't expect many of the children arriving at the border to be able to stay in the U.S.

"It's unlikely that most of these kids will qualify for humanitarian relief," Earnest said. "It means they will not have a legal basis for remaining in this country and will be returned."

Still, it's unclear how quickly that process will unfold. Homeland Security Secretary Jeh Johnson acknowledged Sunday that such proceedings might be long delayed, and he said that coping with floods of unaccompanied minors crossing the border is a legal and humanitarian dilemma for the United States.

"Our border is not open to illegal migration, and we are taking a number of steps to address it, including turning people around faster," Johnson told NBC's "Meet the Press." At the same time, he said, the administration is "looking at ways to create additional options for dealing with the children in particular, consistent with our laws and our values."

Read more at the Associated Press