Obama did not directly mention his health-care initiative when he campaigned Sunday on behalf of Coakley, the state attorney general, who is running to fill the seat once held by the late Edward M. Kennedy. Even before the polls opened, White House officials sought to blunt the narrative that the Coakley-Brown race was a referendum on the president’s health-care legislation, in part because Massachusetts already has universal coverage.

“Massachusetts is completely unique because the health reform law passed a few years ago,” White House communications director Dan Pfeiffer said. “It makes it an imperfect example and impossible to extrapolate.”

Other Democrats argued that Coakley, rather than health-care reform, bears principal responsibility for allowing the race to become so close, noting that in many of their private polls, both the president and his initiative are more popular than is the attorney general.