Josh Earnest the spokesman at the White House said the majority of the children would not have the proper qualifications to remain in the U.S.
Those possibly qualifying for asylum are the children who were victims of abuse in their home. Minors fleeing violence that is gang related would have a more difficult time qualifying, said experts in immigration.
The stern warning came at a time the White House is expecting to release on Tuesday its request for emergency funding from Congress to help with the flood of young children.
The money being requested would go for additional detention facilities to giving the children housing and additional judges for immigration as well as asylum officials so hearings could be expedited.
An official from the Justice Department said the goal was to hire 30 additional judges to tackle the outrageous workload.
However, there likely will be tough times in the U.S. Congress for the measure.
One Republican Senator from Alabama said the measure should only be paid for by cutting other programs in the government.
The senator suggested taking money from the healthcare law to pay for the cost, but Democrats in Congress would likely be opposed.
Over 52,000 minors who have been unaccompanied from Honduras, El Salvador and Guatemala have been detained while attempting to sneak into the U.S. since October.
Many of the kids are fleeing gangs, drug violence and extreme poverty as well as responding to the rumors that have spread about children who make it into the U.S. will be given permission to stay.
On Monday, Ana Garcia the wife of Juan Hernandez the president of Honduras said officials in the U.S. had told her they would start sending flights of families being deported back to the Central American countries starting next Monday.
Obama will visit Texas during the week to raise funds for candidates in the Democratic Party who are running in congressional election in November.