"This heartbreaking exchange says more about the current state of the immigration debate than the remarks of the two presidents in the Rose Garden," said Frank Sharry, executive director of America's Voice, an organization working for immigration reform. "The little girl wants her mother to have papers, but hears that the president is sending people away who don't have papers. She speaks the truth."
A spokesman for the Department of Homeland Security said the department's investigations into immigration status questions are "based on solid law enforcement work and not classroom Q and As."
"ICE is a federal law enforcement agency that focuses on smart, effective immigration enforcement that prioritizes criminal aliens who pose a threat to our communities," DHS spokesman Matt Chandler said.
In what has become a familiar refrain, President Obama today said he supported comprehensive reform but blamed Republicans for refusing to join the effort.
"I don't expect to get every Republican vote," he said, "but I need some help in order to get it done."
ABC News' Polson Kanneth, Stephanie Z. Smith and Jay Shaylor contributed to this report.