The polls say Martha Coakley is the overwhelming favorite to win the Democratic nomination for governor next Tuesday. But as Coakley tries to close the deal, her mood is hardly triumphal.

"I believe that if we invest in our people — if we invest in our kids, we invest in healthcare and mental healthcare, we can turn this economy around for everybody," during a recent appearance at a senior-living facility in Jamaica Plain. "We can make Massachusetts prosperous and fair."

Personality is one factor. Coakley, the state's attorney general, has the buttoned-down demeanor of a career prosecutor. And soaring oratory has never been her stock in trade.

"When I graduated from law school my dad gave me a plaque that said, 'Sometimes the best man for the job is a woman,'" she said in one speech. "And I'd like to be that, your next governor, so thank you very much."

But if Coakley's campaign seems a bit muted, there's another reason.

"This is the people's seat!" former U.S. Sen. Scott Brown ­ exulted after he beat Coakley in the race for Ted Kennedy's old Senate seat in 2010.

Four years on, that defeat still casts a shadow. It's become a case study in what happens when a frontrunner gets complacent. At the state Democratic Convention in June, Coakley tried to put the loss to Brown behind her.

"I know how frustrating that race was for all of you," she said. "It was frustrating for me, too."

Last week, Coakley told me that she has moved on ­and that voters are moving on, too.

"Look, when I first ran, I knew that would be an issue," she said. "I knew I'd have to win every vote. I said there'd be no hand unshook in Massachusetts. I've done that work, and I believe that people see that. And I've gotten asked about it through January, February, March. I get asked about it less and less."

But that doesn't mean Coakley has been forgiven, according to UMass Boston political scientist Erin O'Brien.

"The unwillingness right now to coalesce around her, to say 'We're gonna give you our money, do the [get-out-the-vote]," speaks to the fact that the guys at the table — and it is guys in Massachusetts — haven't embraced her," she said.

O'Brien says Democratic insiders worry that Coakley can't beat likely Republican nominee Charlie Baker in November. According to O'Brien, that anxiety is taking a toll.

"Now we've seen the polls close between her and Baker, and I think Democrats are at fault there," she said. "By not rallying around a candidate that's maintained a double digit lead without the Democrats' support all summer, now we see that lack of support in Baker's numbers going up."

And that's good news for Coakley's Democratic rivals. For them, Coakley's 2010 collapse is a both a reason for hope, and an argument to vote for them next Tuesday.

"Look, the fact of the matter is, Martha Coakley was ahead of Scott Brown by 15 points with 13 days left and she lost by 5 points," said Massachusetts Treasurer Steve Grossman, who won the Democratic convention in June and is running second to Coakley in the polls. "A 20-point swing in a 13 day period. This race is up for grabs."

Don Berwick,­ who ran Medicare and Medicaid for President Barack Obama, and is the most liberal candidate in the race, was asked in a debate what made you more electable than Martha Coakley in November.

"Well, the Democrats that I'm meeting in the primary race are very very worried about losing another big election," he said. "We've got that specter hovering over us."

But the Martha Coakley who's running for governor today may not be the same candidate who lost four years ago. Last week, after Coakley was endorsed by several black ministers, Rev. Jeffrey Brown praised her for turning defeat into an asset.

"In the Senate race, the circumstances were, we didn't hear from her till toward end of the race," Brown said. "She came out early looking for us talking with us asking advice, meeting with us. And showed a real hunger, in my opinion."

More than the hunger last time around?

"More than the hunger I saw last time around," he said.

Still, if that extra intensity helps Coakley land the nomination next week, she'll have one more big hurdle to clear. For Martha Coakley, only a general election victory in November will put the past fully to rest.

Watch the segment on Greater Boston: