PHOENIX — Noemí Romero still shudders when she hears the name Joe Arpaio, the former sheriff responsible for the workplace raid in 2013 when she was arrested and spent two months in jail.

So when President Trump signaled that he was considering a pardon for Mr. Arpaio for his contempt conviction, her memories of trauma flared into outrage.

“Trump is delivering a slap in the face to dignified, hard-working people whose lives were ripped apart by Arpaio,” said Ms. Romero, 25, a former supermarket cashier who now babysits to make ends meet. “Arpaio belongs in jail, getting a taste of his own medicine. Trump wants to put Arpaio above the law, showing they are both about white supremacy.”

Mr. Trump’s expression of support for Mr. Arpaio, the 85-year-old crusader against illegal immigration, has ignited a debate across Arizona about the tactics used to crack down on Latinos, the reactions the strategy spawned in fueling the repudiation by voters who ousted Mr. Arpaio, and the nationalist sentiment stoked by Mr. Trump, one of the former sheriff’s most ardent admirers.