That sense of Mr. Romney looking down his nose at Mr. Perry has intensified the Texas governor’s disregard for his rival, two associates said. Mr. Perry believes that Mr. Romney has been condescending and that he has not taken his candidacy seriously, they said…

But other aides publicly accused the Texas governor of acting like a bully at the debate. “I don’t think road rage is a quality people are looking for in their next president,” said Stuart Stevens, a top strategist for Mr. Romney…

Mr. Romney’s aides said Wednesday that he had gotten the better of his rival. But they also said they welcomed the idea that Mr. Perry might emerge as a more compelling opponent in the weeks to come. Several said the challenge of defeating a stronger Rick Perry would improve Mr. Romney’s shot at winning the White House.

“Of course people took swings at him, but he was passionate,” said Andrea Saul, a spokeswoman for Mr. Romney. “He’s always going to defend his record, he’s not going to take these misrepresentations lying down by any means.”