From left, Attorney General Douglas F. Gansler, Del. Heather R. Mizeur (Montgomery) and Lt. Gov. Anthony G. Brown, the Democratic candidates for governor of Maryland. (Matt Mcclain/AP)

Maryland Lt. Gov. Anthony G. Brown holds a commanding lead over his Democratic rivals for governor, according to a new Washington Post poll, two weeks before a primary election that most voters are not following closely and that is likely to attract a low turnout.

Though nearly half of likely voters say they could still change their minds, the poll found backing for Brown across a broad demographic range — and deep support among fellow African Americans — and showed that Brown voters are firmer in their allegiance than those siding with the other candidates. With scant evidence that attacks on Brown’s management skills, particularly his handling of the state’s health insurance exchange, have damaged him, the poll shows no obvious path to victory for the other Democratic hopefuls in the June 24 primary.

Statewide, 46 percent of likely Democratic voters support Brown, while 23 percent back Attorney General Douglas F. Gansler and 16 percent support Del. Heather R. Mizeur (Montgomery), according to the poll.

Analysts said Brown’s lead is formidable in the race, in which early voting starts Thursday.

“Absent a gigantic mistake from the Brown campaign, this is probably over,” said Donald F. Norris, chairman of the public policy department at the University of Maryland Baltimore County. “I think the only strategy left for a candidate in Gansler’s situation is to attack, attack, attack, and that’s likely to backfire.”

If Gansler is too aggressive, Norris reasoned, he could strike voters as desperate and wind up driving voters to Mizeur as an alternative.

In the Republican primary, Anne Arundel County businessman Larry Hogan leads among likely voters, with the support of 35 percent, the poll found. He is followed by Harford County Executive David R. Craig with 19 percent, Charles County businessman Charles Lollar with 13 percent and Del. Ronald A. George (Anne Arundel) with 5 percent.

In Maryland, where registered Democrats outnumber Republicans more than two to one, Brown would start a general-election campaign against Hogan in a strong position. The Democrat leads the Republican 51 percent to 33 percent among all registered voters in a hypothetical matchup, according to the poll. Both Brown and Hogan attract large majorities of their own party members, but Brown also holds an advantage among independent voters.

Hogan said he would be a stronger general-election candidate than the Post poll suggests, in part because voters so far have been exposed to a much more expensive campaign from Brown. “We’ve spent a few hundred grand,” Hogan said. “They’ve spent millions on television. It’s really not a fair comparison.”

Brown said he is taking nothing for granted in the primary. “We’re going to campaign actively for the next 14 days,” he said. “It’s a breakneck schedule to get to as many communities as we can to talk about our shared vision.”

Gansler continued to hit Brown on Tuesday, telling a group of municipal leaders at a candidate forum in Ocean City that his record of accomplishment stands in stark contrast to Brown’s botched handling of the state’s health insurance exchange.

“I actually rolled up my sleeves,” Gansler said, as Brown sat nearby. “I actually got the work done.”

Gansler spokeswoman Katie Hill said that the campaign’s latest internal polling shows “a significantly closer race” than the Post data suggest. “Brown has yet to close the deal with voters,” she said.

Mizeur campaign manager Joanna Belanger pointed to some positive signs for her candidate in the poll, including the number of voters who could change their minds, and noted that Mizeur’s TV ads started much later than those of her better-funded rivals.

There is a stark racial divide in the Democratic primary, with Brown, who would be Maryland’s first African American governor, holding a nearly 5-to-1 advantage over Gansler among black Democrats. Among white Democrats, the race is a statistical dead heat between the two, with Mizeur trailing. In recent elections, African Americans have accounted for more than 35 percent of Democratic primary voters in Maryland, according to exit polls.

Brown, a former state delegate from Prince George’s County, leads across all age groups, education levels and income levels and in all regions of the state, running strongest in his home jurisdiction. Even in Montgomery County, where Gansler lives and served as state’s attorney, Brown is ahead, although his lead is within the poll’s margin of error.

Tony Berry, 48, a computer technician from Lanham, said he is drawn to Brown in part because he would be the state’s first African American governor and in part because of his military background. He also said he likes the tone of Brown’s campaign, while he has been “turned off” by Gansler’s attack ads.

“We need adults in the room,” Berry said. “We don’t need the attacks. We need solutions.”

In addition to one another, the candidates are battling an unusually apathetic electorate this year. Only 53 percent of Democratic voters say they are certain to vote in the primary, which Maryland has moved to June instead of September. Sixty-eight percent of Democrats said they were certain to vote about this time eight years ago, even though the primary was more than two months away.

Heather Young, a mother of one in her mid-40s who lives in Montgomery Village, is among those voters not tuned in. Young said she votes in almost every election cycle and almost always votes for Democrats. This close to an election, she would normally know enough about the candidates to lock in on a choice. She said she is embarrassed by how little she knows about the upcoming primary — including who is running.

“I’m sort of over politics,” she said. “I feel like the last presidential election really did me in. . . . I don’t want to know everything. It was so negative.”

The Post poll suggests that criticism of Brown’s health-care record is getting little traction. Asked who is mostly to blame for the problems with the insurance exchange, only 10 percent of registered Democrats choose Brown. The most frequently cited culprits are state and federal regulators, who receive a combined 37 percent of the blame.And just 28 percent of registered Democrats say the state’s problems would be a major factor in the way they vote on primary day.

Asked more generally which of the Democrats they consider the best manager, more choose Brown (37 percent) than Gansler (21 percent) or Mizeur (11 percent).

Voters like Jennie Sherwin, 66, are giving Brown the benefit of the doubt on the health insurance exchange, which she noted also had problems on the federal level.

“I would not hold it against him for the same reason I wouldn’t hold the launch of the federal site against President Obama,” said Sherwin, who moved back to Maryland from New Mexico about a year ago and writes a blog about the environment, health issues and alternative therapy.

Echoing an argument that has been made by Brown, Sherwin said the contractors hired by the state to build the exchange deserve blame for the botched rollout.

Gansler’s efforts to tie Brown to tax increases passed during the administration of Gov. Martin O’Malley also are not connecting with most voters, the poll found. Asked which candidate they would trust to do a better job handling taxes, more registered Democrats cite Brown (36 percent) than Gansler (22 percent) or Mizeur (13 percent).

On job creation — another area in which Gansler has criticized the administration and touted his own plans — more registered Democrats say they trust Brown (42 percent) than Gansler (18 percent) or Mizeur (11 percent).

Brown is also more trusted than his Democratic rivals on handling health care, education and crime.

Presented with a list of positive attributes — “is honest and trustworthy,” “understands the problems of people like you” and “has a vision for the state’s future” — more than twice as many voters say each better describes Brown than either of his rivals.

The poll found little support among Democratic voters for cutting the corporate income tax, a Gansler policy proposal on which he parts ways with his two rivals.

Gansler has pushed the idea of reducing Maryland’s corporate income tax rate from 8.25 percent to 6 percent, to match Virginia’s. While Gansler argues that the move would help attract businesses to the state, Brown and Mizeur have said that it would make it harder to fund spending priorities, including pre-kindergarten education.

In the poll, 53 percent of registered Democrats say they oppose cutting corporate income taxes, while 37 percent support the idea.

There is more support for an idea pushed by Mizeur to raise taxes on the state’s wealthy residents.Doing so, she has argued, would allow the state to cut income taxes for most other Marylanders. Sixty-four percent of registered Democrats support raising taxes on incomes over $250,000, while 32 percent oppose the idea, the poll found.

The poll suggests that Mizeur’s candidacy is not getting much lift from her proposal, however. Among those who support the tax increase, Mizeur still runs third behind Brown and Gansler, the poll found.

Robert Tiller, 72, a retired public policy advocate, is among the voters who say they’ve been drawn to Mizeur in part because of her tax proposals. He said he also likes her because she’s “not a career politician” and she has “avoided the mudslinging” in which Brown and Gansler have engaged. He said that electing a gay woman as governor “would send a great message across the nation.”

The impact of a pair of controversies that dogged Gansler’s campaign last fall has lessened, according to the poll. In October, The Post reported that Gansler had ordered state troopers to regularly speed and run red lights when driving him to routine appointments. That same month, the Baltimore Sun published a photograph of Gansler visiting a high school “beach week” party his son attended, where there was apparent underage drinking.

In the new poll, the percentage of registered Democrats saying the trooper report would be a potential factor in the way they vote dropped to 58 percent, from 68 percent when The Post posed a similar question in February. There has been a larger drop-off in Democrats saying the “beach week” episode will be a potential factor, from 60 percent in February to 41 percent in the new poll.

Jim Yutzy, 62, an accountant who lives in Cumberland, said that he’s been impressed by Gansler’s experience as a prosecutor and that he seems “personable” in his television advertising. “He seems like a nice guy who’s conscientious about doing his job,” Yutzy said. He said that among the Democrats, Gansler was “the only one who sounds halfway decent.”

The Post poll was conducted June 5 to 8 among a random sample of 1,202 adult residents of Maryland, including users of conventional and cellular phones. Results from the full survey have a margin of error of plus or minus 3.5 percentage points.

Scott Clement, Jenna Johnson and Paul Schwartzman contributed to this report.