WASHINGTON (AP) — Most of the unaccompanied children who are arriving at the U.S.-Mexico border may end up getting sent back to their home countries.

That word comes today from the White House, which says most of those children aren’t likely to qualify for humanitarian relief that would keep them from being sent home.

The warning was issued as the White House finalized a spending request to Congress, spelling out the additional resources President Barack Obama wants in order to hire more immigration judges and open additional detention facilities. White House officials plan to send the request, totaling more than $2 billion, to lawmakers tomorrow.

Spokesman Josh Earnest says the immigration review process will be allowed to take place, but that most of the children “will not have a legal basis for remaining in this country.”

But it’s not clear how quickly that process will unfold. Homeland Security Secretary Jeh (JAY) Johnson acknowledged yesterday on NBC’s “Meet the Press” that proceedings might be delayed for quite a while. He said coping with the flood of unaccompanied minors crossing the border is a legal and humanitarian dilemma for the United States.

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APPHOTO TXEG118: In this June 20, 2014 photo, immigrants who entered the U.S. illegally depart the bus station in McAllen, Texas. The immigrants entered the country through an area referred to as zone nine. (AP Photo/Eric Gay) (19 Jun 2014)

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APPHOTO TXEG120: In this June 25, 2014 photo, a group of immigrants from Honduras and El Salvador who crossed the U.S.-Mexico border illegally are stopped in Granjeno, Texas. Just since October, the Border Patrol’s Rio Grande Valley sector has made more than 194,000 arrests, nearly triple that of any other sector. Most are from Central America, and many are children. (AP Photo/Eric Gay) (25 Jun 2014)

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