Mr. Brown, who has never held elected office, has found himself outpaced by Senator Jacky Rosen, the low-key and well-financed Democratic incumbent. A debate Thursday night presents a key test.

Fighting from behind in the polls, Brown was combative throughout the hour-long debate against Democratic Sen. Jacky Rosen.

In their sole debate, Nevada Democratic Sen. Jacky Rosen and Republican challenger Sam Brown traded jabs over abortion, immigration, and energy policy — but found common ground on unconditional support for Israel.