The moment captured a central tension that has characterized the past week for Mr. O’Rourke: A presidential candidate whose campaign had stalled was suddenly back in the spotlight — but only because of a tragedy in a city that is core to his personal and political identity…

But Mr. O’Rourke’s allies and advisers hope that his impassioned response to the massacre in his hometown, with flashes of raw anger that match the mood of many Democrats, will prompt voters nationally to give him another look. His remarks calling President Trump a white supremacist, and his cussing out of the news media as he urged journalists to “connect the dots” between the El Paso killings and Mr. Trump’s anti-immigrant language and exploitation of racism, drew praise from both liberals and moderates…

“I’m running for president,” he said firmly, when asked to respond to those pushing a Senate bid. “This community holds so much for the rest of the country. Whether it’s immigration, whether it’s our safety, whether it’s our connection to the rest of the world, whether it’s the fact that we’re on the front line of so many issues that can and will define America.”