Attorney General Martha Coakley continues to hold a commanding lead over her four rivals for the Democratic nomination for governor, according to a new Suffolk University poll that also shows voter opinion shifting dramatically against the state’s nascent casino industry.

As the Democrats running to succeed Gov. Deval Patrick enter a critical week of campaigning ahead of the Democratic Party Convention in Worcester this weekend, Coakley leads her nearest rival, Treasurer Steve Grossman, by 32 points with a 44 percent to 12 percent advantage.

Though support for Coakley has fallen from 56 percent since the last Suffolk University Polling Center survey in February, Grossman’s backing has remained relatively flat with over 32 percent of voters indicating that they are still undecided in the race.

Meanwhile, the overall opinion of casino gaming in Massachusetts has flip-flopped over the past four months, according to the poll. While a majority of Bay State voters approved of casino gaming in February, 47 percent now disapprove of casinos compared to 37 percent who still favor casino gaming. Support for the industry is down from 50.5 percent in February.

The Massachusetts Gaming Commission is poised to decide Friday whether to award the state’s first casino license to applicants MGM who hope to build a facility in Springfield. The commission is scheduled in late August or early September to award a casino license in the Boston area.

The poll arrives ahead of a Herald/Suffolk debate with the five Democratic candidates planned for Tuesday at 11 a.m. The debate will be moderated by Suffolk University’s John Nucci, a former city councilor, and Herald editorial page editor Rachelle Cohen. It will be streamed live on Suffolk.edu, Bostonherald.com, and the newspaper’s internet-based station, Boston Herald Radio.

“The race is a little bit closer in the Democratic primary but it’s still Coakley’s,” said Suffolk University polling director David Paleologos. He said “Coakley’s numbers have dropped a little bit not to anyone else’s benefit.”

Grossman told the News Service that Coakley’s campaign is suffering from a “passion gap,” and predicted that he would begin to close the deficit in both support and name recognition later in the summer when his campaign begins airing ads on television.

“When I saw that poll, frankly, I saw Martha Coakley at 44 percent and I said ‘whoa.’ If you are the clear front-runner, if you’re the acknowledged front-runner, and you can’t make it out of the 40s in a poll that’s a serious challenge and when you have this passion gap to boot with your activists, those are serious, serious challenges,” Grossman said.

While only one license for a slot parlor has been issued so far in Massachusetts, the Gaming Commission is getting close to issuing a casino license in western Massachusetts where MGM is the lone bidder for a license in Springfield. The commission is also considering applications in eastern Massachusetts for a casino in either Everett or Revere, and the Supreme Judicial Court is expected to rule soon whether a proposed ballot question repealing the expanded gaming law is eligible for the ballot in November.

Only 18 percent said they thought it made sense to locate a casino in Revere, while 5 percent said Everett made sense as a location for a Greater Boston casino. Fifty-six percent said neither spot made sense to them.

The shifting opinions on casino gaming could create an opening in the gubernatorial race for former Obama health official Dr. Donald Berwick, who is the only Democrat in the field to oppose casinos and express his support for repeal. After polling at less than 1 percent in February, Berwick saw his numbers in this latest Suffolk survey tick upward slightly to 4 percent, putting him in third place.

Democrat Juliette Kayyem, a former state and federal homeland security official, captured just over 2 percent in the poll, while Wellesley biopharmaceutical executive Joseph Avellone had under 2 percent.

While nearly 37 percent of voters said they were not following the governor’s race very closely or at all, those numbers would probably be significantly higher in the other statewide races where undecided voters make up the clear majority.

Democrats Stephen Kerrigan and Leland Cheung tied at 4 percent in the four-way race for lieutenant governor with more than 85 percent of respondents indicating they were undecided.

Former assistant attorney general Maura Healey leads former state Sen. Warren Tolman 21 percent to 18 percent, with 59 percent undecided, while former Brookline Selectwoman Deb Goldberg (11 percent) led both her Democratic opponents Sen. Barry Finegold (8 percent) and Rep. Thomas Conroy (4 percent).

As Democrats prepare to gather in Worcester for the party’s nominating convention, Grossman is widely expected by party insiders to win the delegate vote despite trailing Coakley in the polls. Coakley, however, remains the only candidate in the race currently polling ahead of expected Republican nominee Charlie Baker.

Coakley leads Baker 36 percent to 29 percent in a hypothectical matchup, while Grossman trails Baker 27-24, within the 3.5 percent margin of error. Coakley’s seven-point lead over Baker is down from 13 points in February, while Grossman has narrowed the gap slightly with Baker that was five points at the time of the last poll.

The independents in the race for governor – venture capitalist Jeff McCormick and health consultant Evan Falchuk – are barely registering with less than 2 percent of likely voters.

“What it says is that there’s a ‘passion gap’ in her campaign that is, I think, very, very potentially damaging to her,” Grossman said of his perceived edge at the convention. “Yeah, she has the lead in the polls. When you have 95 percent name recognition, you’re going to have a lead in the polls, but I’m not worried about that.”

Despite a barrage of negative attention for Gov. Deval Patrick over the past several months, the two-term governor’s approval rating remains strong with 57 percent approving of the job he is doing as governor and 48 percent saying they think Massachusetts is heading in the right direction.

Asked about the Department of Children and Families and told that there have been nearly 50 deaths since 2006 of children under DCF supervision, 38 percent of respondents to the poll blamed Patrick while 27 percent saw the tragedies as on par with what happens in other states and 35 percent were unsure.

President Barack Obama’s approval rating in Massachusetts was about level with 45 percent approving and 44 percent disapproving of the job the president is doing, while 49 percent believe the Affordable Care Act is generally good for Massachusetts compared to 40 percent who view it as generally bad.

Mike Deehan and Gin Dumcius contributed reporting.