Michelle Obama Caught in Immigration Debate

WASHINGTON, May 20, 2010— -- The state dinner Wednesday night for Mexico's President Calderon went as scripted, but the visit was dominated by the thorny issue that has raised heated debate in recent months -- immigration. Even Michelle Obama was pulled into the controversy during a visit with the Mexican president's wife to a local elementary school.

President Calderon called the new immigration law in Arizona discriminatory.

"If we are divided, we cannot overcome these problems," Calderon said at the arrival ceremony Wednesday morning.

President Obama agreed, saying that he shares the frustrations of people unhappy about the inability of lawmakers to pass immigration reform but that the "troublesome" Arizona law could subject people to "harassment."

"I think the Arizona law has the potential of being applied in a discriminatory fashion," Obama said in joint remarks with Calderon.

Michelle Obama, who visited New Hampshire Estates Elementary School in Silver Spring, Md., with Mexico's first lady Margarita Zavala, was caught in a headline-grabbing moment when a second-grader shyly raised her hand. She said: My mom "says Barack Obama's taking everybody away that doesn't have papers."

"Yeah, well that's something that we have to work on, right? To make sure that people can be here with the right kind of papers, right? That's exactly right," the first lady responded.

But then, the student quietly added: "But my mom doesn't have any."

"Well, we have to work on that," Mrs. Obama replied. "We have to fix that, and everybody's got to work together in Congress to make sure that happens. That's right."

Immigration Central Topic in Mexican President's Visit

The issue of immigration is likely to stay front and center as Arizona tries to implement its new law. And although the little girl's mother lives far from Arizona, the school principal later told ABC news her mother was terrified about what her daughter had revealed to Mrs. Obama, and did not want her name released.

A Department of Homeland Security spokesperson told ABC News the mother doesn't have anything to worry about, and that they base investigations on criminal issues, not classroom issues.

"ICE [U.S. Immigrations and Custom Enforcement] 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. "Our investigations are based on solid law enforcement work and not classroom Q&As."

ABC News' Huma Khan and Karen Travers contributed to this story.