State Treasurer Steven Grossman is cutting into Attorney General Martha Coakley's lead in the Democratic race for Massachusetts governor, according to a poll.

Coakley's lead, once as high as 40 points, was 42% to 30%, in a Suffolk University-Boston Herald poll of 400 "very likely" primary voters released Aug. 25. Former Obamacare administrator Donald Berwick has 16% of the Democratic primary vote.

Coakley in 2010 blew a 31-point lead to Republican Scott Brown in an open-seat U.S. Senate election to succeed the late Edward "Ted" Kennedy.

The primary is scheduled for Sept. 9. Democratic Gov. Deval Patrick is not seeking re-election.

Republican Charlie Baker, a health insurance chief executive and former gubernatorial nominee, enjoys a 70% to 11% lead over conservative Mark Fisher.

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