Embattled Rep. John Tierney, D-Mass., leads his Republican challenger in a new poll released early on Wednesday, but the survey suggests that Tierney's support is soft, contributing to his vulnerability.

The poll of likely voters in Massachusetts' 6th District, conducted by the MassINC Polling Group for Boston-based NPR affiliate WBUR-FM, shows Tierney leading former state Sen. Richard Tisei, 46 percent to 34 percent. Seven percent of likely voters said they would vote for the Libertarian candidate, Daniel Fishman, while 12 percent chose another candidate or were undecided.

A 12-point lead is usually considered secure, but the poll suggests Tierney's supporters are not yet committed to his candidacy. That matchup includes "leaners" — respondents who initially said they were undecided, but then said they were leaning toward one of the candidates. In the initial matchup question, just 39 percent said they would vote for Tierney, compared with 32 percent for Tisei.

Tierney, whose wife has been convicted of crimes related to her brother's illegal gambling operation, has a mixed image rating, the poll shows. Thirty-five percent of likely voters have a favorable opinion of him, compared with 30 percent who view him unfavorably and 10 percent who have never heard of him. Tisei, who was Republican gubernatorial candidate Charlie Baker's running mate in 2010, has a more positive net rating — 29 percent favorable, 13 percent unfavorable — but more than a quarter of likely voters said they have not heard of him.

The poll was conducted Sept. 8-10, surveying 401 likely voters via landline and cell phone. The margin of error is plus or minus 4.9 percentage points.

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