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“DHS has spent some money and claims our border is secure. We all know that’s not true,” said Ms. Jones. “Arizona is going to have to lead the way on this.”

Former Rep. Frank Riggs cited Mexico’s involvement in allowing the unaccompanied minors a path to the United States.

“I would mobilize the National Guard to return these immigrants to Mexico and surrender them to the Mexican authorities,” Mr. Riggs said at “Mexico is complicit: They had to know these immigrants were coming across their southern border.”

Former Mesa Mayor Scott Smith held a press conference outside the Border Patrol facility in Nogales, where the children are being housed. “We are facing a humanitarian crisis in Nogales because of a broken immigration system,” he said.

Arizona political analyst Michael O’Neil agreed that immigration is a heated issue for Republicans but warned them against going too far.

“Everyone is moving to see who can move the farthest to the right and be the most anti-Obama,” said Mr. O’Neil. “That’s understandably good politics for the primary, but I’m not so sure about the general. If you come across as too harsh, it could be risky.”

Mr. Obama has described the situation as a “humanitarian crisis.” On that score, he and the Republican candidates agree.

“This is a humanitarian crisis, and we want answers,” said Mr. Ducey. “Barack Obama says the border is more secure than it’s ever been. Obviously, it’s not.”