Attorney General Martha Coakley (42 percent) leads her closest rival, Treasurer Steven Grossman (30 percent) by 12 points, according to a Suffolk University/Boston Herald statewide poll of tightly screened likely Democratic primary voters. Donald Berwick received 16 percent, and 12 percent were undecided.

“Martha Coakley is leading Steve Grossman, but Don Berwick’s share of likely voters continues to grow, and there is a pool of undecided to draw from,” said David Paleologos, director of the Suffolk University Political Research Center in Boston. “To rise to the top, Grossman would have to capture all of the remaining undecided voters while not allowing Coakley or Berwick a single point.”

Demographically, Coakley is running strong against Grossman among women (49 percent to 26 percent), but she trailed Grossman by 1 point (35 percent to 34 percent) among men. Coakley led (44 percent to 27 percent) among registered Democrats, but trailed Grossman (39 percent to 37 percent) among independents who plan to take a Democratic ballot on September 9.

Despite Coakley's double-digit lead, the poll unveiled some challenges for her. Only 8 percent of likely Democratic voters rated Coakley's campaign to date as excellent, while 31 percent said good, 31 percent fair, and 12 percent poor. Forty-six percent said she was a worse statewide candidate than Gov. Deval Patrick, and 53 percent said she was a worse candidate than U.S. Sen. Elizabeth Warren. Coakley's 60 percent favorability rating was higher than both her opponents’ but so was her unfavorability at 22 percent.

Other statewide Democratic races

In other Democratic primary races, attorney general candidate Warren Tolman has opened up a 6-point lead (35 percent to 29 percent) against Maura Healey following a TV ad blitz touting his stances on women’s issues.

In the Democratic race for state treasurer, Deborah Goldberg (20 percent) led Barry Finegold (8 percent) and Thomas Conroy (7 percent) with 64 percent undecided two weeks before the primary.

The Democratic race for lieutenant governor has a 71 percent undecided, and candidates Leland Cheung, Stephen Kerrigan and Michael Lake split the remaining vote evenly.

Commanding lead for Baker, but voters lukewarm

Republican Charlie Baker (70 percent) is headed for a rout of Mark Fisher (11 percent).

“It’s interesting that Fisher can’t reach 15 percent statewide given his fight to get on the ballot and the controversy over whether he had attained the required 15 percent of delegates at the Republican convention earlier this year,” said Paleologos.

Despite his popularity and strong predicted showing in the primary, Republican primary voters said that Baker was a worse candidate than both Mitt Romney and Scott Brown, who lost to Senator Elizabeth Warren in 2012. Only 8 percent of likely Republicans rated Baker’s campaign to date as excellent while 43 percent indicated good, 24 percent said fair, and 5 percent said poor.

“Even the ‘best of the best’ party primary voters appear to be lukewarm toward Coakley on the Democratic side and toward Baker on the Republican side,” said Paleologos.

2016 presidential sweepstakes

Massachusetts Republican voters are split among New Jersey Gov. Chris Christie, Congressman and 2012 vice presidential nominee Paul Ryan (R-Wisc.), former Florida Gov. Jeb Bush, and Sen. Rand Paul (R-Ky.), who were all tied at 11 percent.

When Mitt Romney was added into the mix, he dominated the field among likely Republican voters, securing 49 percent while driving all other potential candidates into single digits.

On the Democratic side, Hillary Clinton was the first choice for 55 percent, followed by Elizabeth Warren with 17 percent and Vice President Joe Biden with 8 percent.

Methodology

The statewide Suffolk University survey of Democrats used a call list of voters from at least three of the past four statewide Democratic primaries, including the 2002 and 2006 Democratic primaries for governor and the 2009 and 2013 special Democratic primaries for U.S. Senate. On the Republican side, the list used was the last contested statewide Republican primary for U.S. Senate in 2013. All respondents indicated that they were very likely to vote in and could identify the date or timeframe of the upcoming party primaries on September 9. Each survey of 400 likely voters was conducted Thursday, Aug. 21, through Sunday, Aug. 24. The margin of error is +/-4.9 percent at a 95 percent level of confidence. Results will be posted on the Suffolk University Political Research Center website at 1 p.m. Aug. 25. For more information, contact David Paleologos at 781-290-9310, dpaleologos@suffolk.edu.