That’s what Keith Brockenberry, a cook, wanted to know at a meet-and-greet in Roxbury last week. After one of Ms. Stein’s supporters clarified, “for president of the United States,” Mr. Brockenberry seemed both taken aback and delighted.

“Get out of here!” he blurted out. “I had no idea.”

What Ms. Stein lacks in name recognition, however, she is trying to make up for these days in high-energy organization and low-cost social media outreach. When she officially accepts the nomination at the Green Party’s convention this weekend in Baltimore, she will be the party’s first candidate to have qualified for federal matching funds — a milestone for this 11-year-old alternative party and potentially a major boost for a campaign that does not accept corporate donations.

The Green Party of the United States expects to be on the ballot in at least 45 states and to spend about $1 million on its campaign. At the moment, it has secured ballot access, an organizational test in itself, in 21 states, including the battlegrounds of Colorado, Florida, Michigan and Ohio, where the major party candidates, President Obama and Mitt Romney, who are raising tens of millions of dollars every month, are locked in a tight race.

While Ms. Stein barely registers a blip in national polling, experts point to Ralph Nader, the Green Party nominee in 2000, who was seen by many Democrats as siphoning just enough votes from Al Gore in one state, Florida, to tip the election to the Republican, George W. Bush. Nationally, Mr. Nader had captured only 3 percent of the vote.

Could such a situation unfold again?

Unlike Ms. Stein, a physician on leave from her practice, Mr. Nader, a lifelong consumer advocate, enjoyed high name recognition. But now, more than a decade later, the Green Party has matured to the point at which Ms. Stein’s lower profile may be balanced by a more savvy political operation.

“The Green Party only needs to pull a very small number to provide an upset in a state like Ohio, if the balloting is close,” said Peter Ubertaccio, chairman of the department of political science and international studies at Stonehill College, in Easton, Mass. “Then suddenly their insignificant overall numbers become hugely significant in deciding who gets the electoral votes in that state.”

It’s a danger to their natural allies, the Democrats, he said.
Ms. Stein, 62, a graduate of Harvard College and Harvard Medical School, takes her ultra-long-shot odds in stride and is eager to explain to anyone who will listen “how a nice doctor like me,” she says, “got to be in a Godforsaken place like this.”

A general internist who grew impatient with the social and environmental roots of disease, Ms. Stein said, “I’m now practicing political medicine because politics is the mother of all illnesses.”

The Green Party’s supporters tend to be young, but the party is also popular with liberals of all ages who are disenchanted with the Obama administration.

Emily Winter, 24, is one such voter. “I voted for Obama because he preached change, and he’s done impressive work in the area of women’s rights, heath care and foreign policy,” said Ms. Winter, a Boston University graduate student who approached Ms. Stein on a South End street to ask for a photo. “But I feel like too many other policies are stuck where they’ve been for years.”

Ms. Stein, ever polished in bright scarves and slim pantsuits, is quick to point out that she is the only candidate who has experience debating Mr. Romney, which she did in the 2002 Massachusetts governor’s race, her first of four unsuccessful attempts at elected office.

What did she learn? “It’s easy to debate a robot,” she said of his speaking style.

While Ms. Stein ultimately lost big, with only 3 percent of the vote, a poll taken by a local television station immediately after one debate showed that 32 percent of voting viewers said she had won the debate, compared with 33 percent who gave it to Mr. Romney (he ultimately won the race).

“Stein wouldn’t have struck you, if you were watching the debates, as a caricature of a third-party candidate,” Professor Ubertaccio said. “She was thoughtful and spoke about policy quite knowledgeably.” Still, some detractors dismiss Ms. Stein as a perennial protest candidate who has never gained much traction with voters.

Now a major challenge for Ms. Stein, a native of the Chicago area who lives northwest of Boston with her husband, a surgeon (they have two adult sons), is to show that she can win support around the country. She longs to be included in the nationally televised debates, a high hurdle for any third-party candidate. According to the Commission on Presidential Debates, a candidate must have “a level of support of at least 15 percent of the national electorate” as determined by five national polling organizations.

Ms. Stein’s problem, then, is of the chicken-and-egg variety: to get national name recognition, she needs television exposure in debates. But she does not qualify for debates because of a lack of national name recognition.

She thinks that is by design, to benefit major parties.

“If they actually have to debate a living, thinking, informed person, it’s very hard for them,” Ms. Stein added, referring to Mr. Obama and Mr. Romney. “They have kind of a mutual agreement, which you can see evident in the nature of their debate right now. If it’s important, they won’t go there. Many issues are not on the table.”

Ms. Stein says she emphasizes issues like ecological sustainability, racial and gender equality, and economic justice. The centerpiece of her platform is a Green New Deal, a twist on the Roosevelt-era programs intended to stimulate job growth and the depressed economy. It could be paid for by ending the presence of American troops in Iraq and Afghanistan, the campaign says, and by eliminating waste in the health care system. Beyond that, Ms. Stein favors a progressive income tax that would raise rates on the wealthy.

“There are overwhelming benefits to moving to a green economy that provides jobs and good wages,” she said.

Ms. Stein is quick to align Mr. Obama and Mr. Romney, saying their policies are nearly indistinguishable. She cites the former governor’s policy on health care and the president’s health overhaul as an example. (She supports a single-payer system.)

“We need to have people in Washington who refuse to be bought by lobbyist money and for whom change is not just a slogan,” Ms. Stein said. “It seems like there’s a rebellion going on, and people are really ready for something different.”