The four Democrats in the Massachusetts Senate race have been scrambling to rally a largely uninterested electorate to go to the polls for Tuesday’s special election primary.

Brian McNiff, communications director at the Massachusetts secretary of State’s office, estimated that as few as 300,000 to 500,000 of the more than 4 million registered voters may turn out for an election that has failed to capture the public’s attention ­— even though it will determine a permanent successor to the late Sen. Edward Kennedy (D), a political icon nationally and particularly in Massachusetts.

The winner of the Democratic primary is heavily favored to win the general election on Jan. 19 against the likely Republican nominee, state Sen. Scott Brown.

Brown is expected to handily defeat Jack E. Robinson, a businessman and frequent GOP candidate in Massachusetts.

Massachusetts Attorney General Martha Coakley was the first to jump into the Democratic primary field and has maintained the lead ever since, conducting a cautious frontrunner campaign and giving her rivals few opportunities to close the gap.

Rep. Mike Capuano, Alan Khazei and Stephen Pagliuca have held back from attacking fellow Democrat Coakley directly, resulting in a contest that has been high on consensus and low on drama.

“It’s not a race that’s generating a great deal of buzz and electricity,— said Jim Gomes, director of the Mosakowski Institute for Public Enterprise at Clark University in Worcester, Mass. Gomes surmised that is “because it’s a special election, because the candidates have a lot of overlap in their issue positions, because none of the candidates have really gone after the others in a serious way.—

He noted that the Democrats have not run one truly negative ad — a departure from the norm in heavily contested races.

Instead of going after Coakley, her opponents have sought to staunch her aura of inevitability in the race’s final stretch by ramping up their voter outreach and rolling out a series of high-profile endorsements.

Capuano, who has been running second behind Coakley in the latest polls, received the backing of former Massachusetts Gov. Michael Dukakis; Rep. Ed Markey (D-Mass.), dean of the state’s all-Democratic delegation; and the Boston Herald. Khazei, co-founder of the national community service program City Year, was endorsed by the Boston Globe, Worcester Telegram & Gazette and former NATO Supreme Allied Commander and 2004 Democratic presidential candidate Gen. Wesley Clark.

Lacking any big endorsements, Pagliuca, a managing director at Bain Capital and co-owner of the Boston Celtics basketball team, featured the Celtics’ NBA championship trophy on his weekend tour of the state.

The Khazei campaign has sought to portray Khazei as the Kennedy candidate, distributing a photo of him posing with Caroline Kennedy at a campaign fundraiser hosted by New York Mayor Michael Bloomberg, a Khazei supporter, as well as a Huffington Post piece by Vicki Strauss Kennedy endorsing Khazei.

Strauss Kennedy’s husband, Max Kennedy, son of the late Robert F. Kennedy, also has endorsed Khazei.

Sen. Kennedy’s widow, Vicki Reggie Kennedy, refrained from making an endorsement.

The Coakley campaign responded with its own flurry of endorsement announcements over the weekend, including seven regional daily papers, feminist activist Gloria Steinem and a number of current and former state officials. That was capped by a nod Sunday night from former President Bill Clinton, who recorded a robocall that went out to 500,000 primary voters on Monday.

All four campaigns are seeking to mobilize their bases of support, hoping that their ground operation will outdo their opponents’ on a day that is forecast to be cold but clear.

Democratic strategists, however, say that Coakley is likely to have the edge in the ground game given her past statewide campaign and her support from a coalition of labor and women’s groups, the latter of which is particularly energized to elect Massachusetts’ first female Senator.