It’s the defining dilemma of the current election season: After eight years in office, Gov. Deval Patrick remains wildly popular; but as the battle to succeed him heats up, the list of problems that can be linked to the Patrick administration continues to grow — including the troubled Health Connector website and deep dysfunction at the state’s Department of Children and Families. Now, the Democrats running to replace Patrick have to strike an awkward balance between running on his record — and running away from it.

On a recent weekday afternoon, gubernatorial hopeful Don Berwick worked a sleepy roomful of senior citizens in Brighton. In his stump speech, the Democrat offered a sobering assessment of the Commonwealth.

"All over the state we’ve neglected transportation," Berwick said. "Bus transportation, regional transit authorities. Just like we’ve neglected building affordable housing!"

To fix those problems, Berwick added, he’s the kind of guy you want in the governor’s office.

"I believe I can bring to this race the competence, the management, and the leadership that’s going to make things better in our state," he said.

That sounds like a dig at Patrick, who’s run the state for eight years. But ask Berwick about Patrick by name and his tone shifts — a lot.

"I worked with governors all over the country when I was running Medicare and Medicaid, and I didn’t see a better governor in the nation than Gov. Patrick," he said. "I think he’s done a remarkable job."

Among other things, Berwick lauds Patrick’s focus on education and clean energy. And he’s not the only candidate who pans parts of the governor’s record, but praises the governor himself.

"I’m running for governor because I believe Massachusetts can now turn this economy around for everybody," said Democrat Martha Coakley during a recent appearance in Jamaica Plain. "Not just Wall Street, not just people at the top, and as I’ve said, not just Boston and Cambridge — I want this for the whole state."

That’s a damning assessment of the state economy. But when I gave Coakley a chance to criticize the governor directly, she took a pass.

"I would give the governor very high marks, in a tough, tough economy, to make sure he kept his eye on what we needed to do: invest in innovation, infrastructure, education," she said. "How do we keep that moving? I think people feel that we’re on the right track."

And then there’s Steve Grossman, the third Democrat running for governor. In contrast to his opponents’ sharp takes on the political status quo, Grossman is downright bullish on what Patrick has wrought.

"The history of Deval Patrick’s leadership will be written as one of a guy with vision, who never lost faith in the people of Massachusetts," Grossman said. "And even in the worst of times, he had faith and acted on it."

Not that Grossman doesn’t have his own quibbles, including the troubled Health Care Connector website and the halting implementation of the state’s medical-marijuana law. But he adds: "These individual moments of concern, perhaps from a leadership or administrative standpoint, I think pale in comparison with the fact that, as you look back, just in the recent past — 14,000 jobs last month! 67,000 jobs in the last year!"

As Grossman, Coakley and Berwick woo the same primary voters that elected Patrick twice, it probably makes sense not to call the governor out by name. Come the general election, though, one of them will probably face Republican Charlie Baker — who’s been honing his critique of Patrick for months. At that point, the Democrats’ delicate dance could turn off voters who want real change.