Many Senate observers, even those close to Mrs. Clinton, say they believe she set the less-than-collegial tone. But Mr. Obama offered a glimpse into his own competitiveness two years ago when a Chicago television reporter who had come to Washington to interview Mr. Obama informed him that he had snagged a hallway interview with Mrs. Clinton.

"I outpoll her in Illinois," Mr. Obama said. After realizing his remark had been overheard, he said: "That was a joke!"