Tucker Carlson set the trap, and Senator Ted Cruz of Texas walked right into it.

“How many people live in Iran, by the way?” Mr. Carlson, the former Fox News host and a longtime ally of President Trump, asked Mr. Cruz, who has become a stalwart supporter of the president’s evolving approach to the conflict between Iran and Israel.

“I don’t know the population,” Mr. Cruz said.

Then Mr. Carlson went in for the kill: “You don’t know the population of the country you seek to topple?”

The confrontation, 97 seconds of which Mr. Carlson posted on X Tuesday night, quickly racked up tens of millions of views and came to embody a rupture that has burst into view on the right, as Mr. Trump weighs sending American aircraft and weapons to support Israel’s efforts to demolish Iran’s nuclear program.

Such a move would represent a remarkable reversal for Mr. Trump, who just months ago opposed military action while he sought a diplomatic solution — and, according to an increasingly vocal chorus of his critics on the right, a reversal of his long-held promise to steer the nation out of, not into, foreign entanglements.

It’s erupted into a fight over the meaning of the Make America Great Again movement, and whether the most fervent keeper of its flame is Mr. Trump’s original base and the isolationism that animated it or the Republicans who back whatever action he takes in the moment.