A distinct lack of visible sweat on the Illinois senator triggered questions about whether he was actually exercising or using the gym visits as cover for conducting vice presidential vetting or interviews. Obama spokesman Bill Burton e-mailed a succinct, two-word answer: “Working out.” That view held credence among some of the photographers who regularly accompany Obama. They said that even when he shot hoops earlier this year with members of the University of North Carolina varsity men’s basketball team, they didn’t see Obama sweat.