ANNAPOLIS, Md. — As a bill legalizing same-sex marriage in Maryland hurtles toward a vote in the legislature this week, a coalition lobbying for its passage has focused much of its efforts on a group of Democrats who could potentially scuttle its success: African-Americans.

It is the most serious attempt by advocates for same-sex marriage to win over blacks, who have traditionally been skeptical, and whose support is critical for the bill’s passage in this state, where nearly a third of the population is African-American, a far higher share than in the broader population.

The campaign includes videos of well-known African-Americans, including Michael Kenneth Williams, an actor from the television series “The Wire,” and Mo’nique, a Baltimore-born actress; an editorial in The Afro; and conversations in churches and union halls, where most members are black.

The Human Rights Campaign and the Service Employees International Union have sent dozens of workers and volunteers, many of them African-American, across the state to talk about the issue. Particular attention is being paid to Baltimore and Prince George’s County, organizers said, two majority-black areas where skepticism has been strong.