Beto O'Rourke and Julian Castro argued over immigration policy.
ABC13 reporter Tom Abrahams was reporting live from the debate.
They pointed to the searing photos of the Salvadoran father and his toddler who drowned in the Rio Grande and blamed Trump and his policies concerning migrants crossing into America illegally.
"Watching that image of Oscar and his daughter Valeria was heartbreaking," said Castro, President Obama's former administration housing chief. "It should also piss us all off."
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Castro's argument centered on repealing Section 1325 of the Immigration and Nationality Act, which was used by the George W. Bush administration to apply a criminal violation as opposed to a civil infraction to anyone entering the United States illegally.
The decades-old law was used by the Bush administration to attempt to curb the number of illegal entrances into the United States, something that Castro said needs to be repealed.
He also assailed O'Rourke for not calling for fully decriminalizing crossing the U.S.-Mexico border illegally.
"I just think it's a mistake, Beto," he said, adding that O'Rourke would agree with him, "if you did your homework on this issue."
O'Rourke says he doesn't support fully decriminalizing such border crossings because of fears about smugglers of drugs and people.
O'Rourke responded to Castro in the spin room after the debate.
"I think we have the same goal. I think he's got it wrong on how he describes my position. I'm focused on the big picture: making sure our laws reflect our values, our interests, and what we know to be right in this country of immigrants, asylum-seekers and refugees," O'Rourke said.
And on Castro saying that he hasn't done he homework, O'Rourke responded: "Well, he's wrong on this one."
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The Associated Press contributed to this report.
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