Rep. John Tierney (D-Mass.) led his Republican challenger, former state Sen. Richard Tisei, by 12 points in a new independent poll. But Tierney, who has suffered politically from revelations about his wife’s family’s gambling ring, is burdened with some significant weaknesses, the survey showed.

Tierney got 46 percent compared with Tisei’s 34 percent in the WBUR poll of likely voters that included leaners conducted by the MassINC Polling Group. Eleven percent were undecided, and 7 percent said they would vote for the Libertarian candidate.

When leaners were not included, Tierney’s lead over Tisei was 7 points.

But red flags abounded for the eight-term Congressman in this poll. Only 35 percent of those polled had a favorable opinion of him — a low number for a longtime Member — while 30 percent had an unfavorable view. Twenty-one percent had heard of him but were undecided, and 10 percent had never heard of him.

Tisei remains less well-known. Twenty-nine percent of those surveyed had a favorable opinion of him while 13 percent had an unfavorable view. A quarter of those surveyed had heard of Tisei but were undecided on their view of him, while 26 percent had never heard of him.

Despite Tisei’s lower name identification, more people thought the phrase “is honest and forthright about important issues” better described him than the Democratic incumbent. Only 19 percent of those polled thought that phrase better described Tierney; 26 percent thought it better described Tisei.

Probably not unrelated: 57 percent of those polled had heard a great deal or a fair amount about Tierney’s family’s legal problems.

Tierney, an attorney, has not been accused of any wrongdoing.

Also of note in the poll: 26 percent of respondents thought the phrase “knows how to get the economy moving again” better described Tisei than Tierney. Twenty percent thought it better described the Congressman than the challenger.

But Tierney bested Tisei on “will stand up for regular people when in Congress,” “understands the needs of middle-class families” and “agrees with you on key issues that matter to you.”

President Barack Obama led GOP nominee Mitt Romney in the poll by 10 points, 47 percent to 37 percent. That means Tisei has a lot of work to do among voters who are likely to go Democratic at the top of the ticket.

The air wars have already heated up in the district. Tierney launched his first TV ad today, and a Republican super PAC has been airing a scathing attack ad against Tierney.

The MassINC Polling Group surveyed 401 likely voters in the district from Sept. 8-10, using live interviews on landlines and cellphones. Party registration among those surveyed was 29 percent Democratic, 15 percent Republican and 56 percent unenrolled in either party. The margin of error for the poll was 4.9 points.