The negatives probably reflect views about his older brother, George W. Bush, whose presidency ended six years ago. “All they know” about Jeb, Mr. Murphy said, is that “he is the brother.” Unsettling to some other Republican strategists is that the Bush brand itself might be problematic. The record of Jeb Bush’s father, the 41st president, George H.W. Bush, has been re-evaluated more positively: He is credited with expertly managing the end of the Cold War, the successful first Iraq War, a budget deficit deal and passing the Americans with Disabilities Act. But those are distant memories for many voters, unlike George W. Bush’s presidency.

The 43rd president remains decidedly less popular than Bill Clinton, his predecessor. In a Quinnipiac University poll last year that asked who was the best of the dozen post-World War II presidents, George W. Bush tied for last place with Richard M. Nixon and Gerald R. Ford, each chosen by only 1 percent of those surveyed.