Ms. DeFranco has made it this far with about $40,000 in donations, according to the most recent campaign filings, and some 40 volunteers, including her husband and mother but also a number of people who met her over the last year. Ms. DeFranco’s campaign also hired a handful of professional signature gatherers to help reach the 10,000 required under state law, she said. Ms. Warren has raised more than $15 million.

John Walsh, the chairman of the Massachusetts Democratic Party, said Ms. DeFranco would almost certainly get enough delegate votes at the convention to make the ballot. The front-runner would have to get more than 85 percent of the delegate vote to knock primary challengers out of the race, something that has not happened since 1982, he said.

“My own belief is that competition is good and healthy and makes us stronger,” Mr. Walsh said. “I hear there are a lot of people who have a different opinion, and what’s going to happen on the floor of the convention hall is you will have 4,000, 5,000 delegates weighing that question.”

Ms. DeFranco is to the left of Ms. Warren on a number of issues, including health care (she supports a single-payer system) and national security (Ms. Warren is more hawkish). She thinks Ms. Warren is too focused on the need for financial regulation — a “one-trick pony,” as Nancy Weinberg, a DeFranco supporter from Newbury, put it during a conversation here.

Ms. DeFranco tartly dismissed Ms. Warren’s recent call for Jamie Dimon, the chief executive of JPMorgan Chase, to resign from the board of the Federal Reserve Bank of New York after his company revealed that it had lost at least $2 billion in bad trades. “Who’s not going to be for firing Jamie Dimon?” she said. “It’s kind of like a throwaway. Tell me what you’re going to do that’s going to change the average person’s life in Massachusetts.”