In the grand digital tradition of American political debates, the audience tends to seize upon singular phrases or gestures that, at least for a few hours, seem to define the evening’s discussion.

After Tuesday evening’s vice-presidential debate between Senator Tim Kaine of Virginia and Gov. Mike Pence of Indiana, it was clear “that Mexican thing” had become a phrase of choice.

“When Donald Trump says women should be punished, that Mexicans are rapists and criminals, or John McCain’s not a hero, he is showing you who he is,” Mr. Kaine said, after repeated efforts during the 90-minute debate to try and persuade Mr. Pence to explain or defend Donald J. Trump’s past comments about immigrants.

“Senator, you’ve whipped out that Mexican thing again,” Mr. Pence replied. “He — look ...”

“Can you defend it?” Mr. Kaine said.