Obama "has tools in his toolbox" to solve quickly what most officials say has become a humanitarian crisis and to deter more children from coming to the U.S., Rogers said.
"We can safely get them home," Rogers said on NBC's "Meet the Press." He said, "And that's where the president needs to start. So he needs to re-engage, get folks who are doing administrative work on the border. They need to make sure they send a very clear signal."
Democratic Sen. Dianne Feinstein of California, the author of the provision in the human trafficking law, said a change in regulations, not the law, could speed the children's return.
The law already allows the departments of Homeland Security and Health and Human Services to write regulations to deal with "exceptional circumstances" that would allow officials to return the children more quickly to their home countries, Feinstein said.
"I would urge HHS and DHS to sit down and set the exceptional circumstances it may be the number of children coming through in a week or a month, however you see it and how the process might be modified to give you more time," she said Thursday during a Senate Appropriations Committee hearing on a $3.7 billion emergency budget request from the White House to deal with the growing crisis on the border.
Feinstein did not elaborate on what changes to the current system she believed the law already allows the president to make.
Under the current law, the Homeland Security Department hs 72 hours to transfer child immigrants traveling alone to the Health and Human Services Department's Office of Refugee Resettlement.
Amid the crush of children traveling alone, more than 39,000 other people traveling with their families, mostly mothers and young children, have also been caught in South Texas. An undisclosed number have been released into the community with notices to report back to immigration officials or in court at a later date.
Obama said the $3.7 billion in emergency spending would help the government deal with the flood of unaccompanied child immigrants crossing the border in South Texas. Some of the money would go to help fund about 40 additional immigration judge teams.
Federal immigration courts have a backlog of more than 375,000 cases. It can often take several years for an immigrant to receive a final ruling.
Republicans have balked at the size of Obama's spending request, arguing that he needs to do more to secure the border and do more to stop immigrant children from making the trip from Central America in the first place.