Mitt Romney is working hard to make voters dislike Newt Gingrich and President Barack Obama. But Mr. Romney has yet to crack a tougher nut: persuading voters to like him.

The likability challenge has dogged the former Massachusetts governor for years. Voters applaud his competence, his business record and his image as a family man. “But it has been very hard for him to translate all that into likability,” said Sally Bradshaw, a Florida GOP strategist who helped manage the Romney campaign there in 2008 but is unaligned this year.