Massachusetts Democrats have nominated a candidate to replace Ted Kennedy, and all indications are that she will be a replacement in full.

Massachusetts Attorney General Martha Coakley ran her primary campaign as an unapologetic progressive who promised to carry on where Kennedy left off on issues ranging from advancing health-care reform to protecting civil rights and opposing unwarranted military adventures abroad.

Coakley framed her run as a campaign to extend the legacy and the mission of the man she referred to as “our distinguished and tenacious Senator Ted Kennedy.”

In announcing her candidacy for the seat held for almost 37 years by Kennedy, she said of the liberal lion of the Senate, “We have depended upon him in the Commonwealth and in Washington for his leadership, his strength, and his sense of humor. As some have noted, we perhaps cannot fill his shoes, but must strive to follow in his footsteps.”

That message carried the day in Tuesday’s special Democratic primary election, which saw the veteran prosecutor winning almost 50 percent of the vote statewide against three serious challengers. It also positions her as the clear front-runner going into a January 19 special election contest with Republican state Senator Scott Brown, a fiscal conservative who the Boston Globe says “falls well to the right of the moderate Yankee Republican tradition, once upheld in the Senate by Massachusetts’ Ed Brooke, Connecticut’s Lowell Weicker, and Rhode Island’s John and Lincoln Chafee.”

That’s not a recipe for success in Massachusetts, which remains one of the most liberal and steadily Democratic states in the nation.

The Democratic primary was always seen as the biggest test for Coakley. And she passed it with ease.

The primary campaign was a struggle between Coakley, the front-runner from the start and a favorite of activists and voters who want Massachusetts to send a woman to the Senate, and Congressman Michael Capuano, a self-identified “passionate progressive” who holds the House seat once occupied by Ted Kennedy’s brother John.

Coakley and Capuano shared positions on most issues — both, for instance, were critics of President Obama’s moves to expand the U.S. presence in Afghanistan, and both were determined advocates for realizing Kennedy’s “health-care-for-all” vision.

The difference between the two candidates in many senses stylistic, with the congressman pointedly condemning insurance companies and big banks and promising to hold former Vice President Dick Cheney to account.

Those populist positions won Capuano support from a number of unions and activist groups such as Progressive Democrats of America.

But Coakley also drew union support, along with strong backing from groups such as National Women’s Political Caucus and Emily’s List.

After Coakley’s primary win, Emily’s List president Ellen Malcolm said, “This is not just an opportunity to add a highly qualified pro-choice Democratic woman to the Senate. Given the climate in Washington right now surrounding a woman’s right choose, the importance of Martha winning this election has been amplified. We look forward to working with her to win the general election in January, making her the first woman to ever represent Massachusetts in the United States Senate.”

Coakley would, if elected, be the first female senator from Massachusetts.

But it was not merely her appeal as the only woman in the Democratic primary contest that put Coakley in a commanding position from the start of the race.

She was the only statewide elected official in the running.

And she had a track record with populist appeal.

Coakley had plenty of cards to play when it came to the economic debate.

As attorney general, she earned a reputation for pursuing corporate accountability. As a candidate, she promised to hit the ground running in the fight to — as she put it — “rebuild our economy so that it works for all of us – not just a privileged few.”

Coakley’s message carried the day. With almost all the precincts reporting, she had 47 percent of the vote to 28 percent for Capuano. Boston community leader and activist Alan Khazei, who was endorsed by the Boston Globe, was winning 13 percent. Boston Celtics co-owner Stephen Pagliuca, who spent heavily from his personal fortune and campaigned as a moderate who would support President Obama on key issues, was attracting 12 percent.

The fact that the candidate who ran closest to Obama finished last is worth noting. Coakley, Capuano and Khazei all positioned themselves to the left of the Obama administration on issues ranging from the Afghanistan buildup to health-care reform.

For her part, Coakley said prior to President Obama’s decision to expand the U.S. troop presence: “I believe we should begin the process of bringing our troops home.”

She also came out as a far more aggressive backer of gay and lesbian rights than the president, with her campaign highlighting the fact that: “Martha has stood as a national leader in defending same-sex couples and their right to marriage. Martha is the only Attorney General in the country to file a lawsuit challenging the constitutionality of the discriminatory Defense of Marriage Act, which unfairly excludes married same-sex couples and their families from critically important rights and protections.”

“In Washington,” her campaign declared, “Martha Coakley will continue this fight and will lead the effort to repeal DOMA.”

In so doing, she will pick up precisely where Ted Kennedy left off.