A governor’s councilor from Gloucester has been gauging support from party activists for a potential challenge to state Democratic Party chairman Thomas McGee, several people familiar with the conversations said.

Eileen Duff, a real estate agent, has contacted state party committee members in the past several weeks to measure whether she could round up sufficient support before the post-election November committee meeting. Several Democrats said additional candidates could also emerge.

Contests for the state party leadership role are rare. Chairmen frequently cobble together consensus support and run unopposed.

General turbulence within the state Democratic Party, not an infrequent occurrence, has mounted this year amid the contentious presidential primary between eventual nominee Hillary Clinton and Senator Bernie Sanders, and over the party’s ideological trajectory.

Democrats have also split over whether Massachusetts should expand the number of charter schools in the state. And a rift between House and Senate lawmakers has endured beyond the July 31 end of the legislative session.

Duff, though, is a Clinton supporter, like McGee. She appears to be trying to latch onto dissatisfaction within the party over McGee’s leadership style.

According to people who have spoken to Duff, part of her pitch has been that she can approach the chairmanship as a full-time job, arguing that McGee has been conflicted by his legislative role.

Other Democrats have complained that the party has not been aggressive enough in opposing Republican Governor Charlie Baker. That unrest burbled up at the state party convention in June, when some activists criticized party leadership for not having a plan to hold the governor accountable.

Two former candidates for lieutenant governor have also been widely mentioned as potential candidates.

Stephen Kerrigan, the party’s 2014 Democratic nominee for lieutenant governor and the CEO of the 2013 presidential inauguration committee, declined to comment.

Mike Lake, a state committee member who ran unsuccessfully in the Democratic primary for lieutenant governor in 2014, was publicly vocal in his criticism at the Lowell confab. He, too, declined to comment.

Until an escalation of its rhetoric in recent days, the party has taken a fairly hands-off approach toward Baker.

The party recently pounced on a scandal within the Baker administration, first reported by WCVB-TV, incited when state officials used taxpayer money to throw a party at the home of a top Republican official.

Duff, who is a state committee member by dint of the seat on the Governor’s Council she won in 2012, declined to comment.

Marsha Finkelstein, a committee member and chairwoman of the Salem Democratic committee, called Duff “talented, smart, and one of the hardest-working Democrats that I know. And if she’s putting her hat in the ring, it’s because she believes she can do a great job.’’

Finkelstein, who declined to say whether she was assisting Duff in her efforts, added, “This is not about Tom. This is about the Democratic Party and what’s in the best interest of the party as a whole moving forward.’’

McGee, through party officials, declined to comment.

Jim O’Sullivan can be reached at jim.osullivan@globe.com. Follow him on Twitter at @JOSreports.