From George Bush to his two political sons, the Bush family has always been squeamish about messy, personal attacks on rivals, preferring to outsource the dirty work to aides.

But now, in an election cycle where the Republican Party’s grass-roots wing is angry and looking for a presidential candidate who projects a visceral sense of their frustration, some of Jeb Bush’s supporters say he may need to learn the fine art of negative campaigning.

The Republican debate on Tuesday in Las Vegas provides Mr. Bush with a highly anticipated platform to forcefully take on his rivals. After faltering in a previous debate exchange with Senator Marco Rubio, Mr. Bush — perhaps more than anyone else onstage — might be compelled to prove he has the strength and passion not just to lead the nation, but to hold his own in the aggressive Colosseum of modern politics.

That could be tricky for a man whose family code is one of polite gentility and even bipartisanship, not angry yelling and boorishness.