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BOSTON — A buoyant Hillary Clinton plunged into the crowd here after a barnstorming speech, posing for selfies and shaking hands on the eve of what she hopes will be a pivotal victory in the 11 states, including Massachusetts, that hold Democratic nominating contests on Tuesday.

Polls show Mrs. Clinton with an edge in Massachusetts, which many analysts say is a must-win for her rival, Senator Bernie Sanders of Vermont.

Sensing that the nomination may be within her grasp, Mrs. Clinton seemed eager here to bring the fight to the Republicans. She referred briefly and obliquely in a 30-minute speech to her “esteemed opponent” without naming him and focused instead squarely on the Republicans, without naming any of them either.

“The stakes couldn’t be higher,” Mrs. Clinton said to 650 people of all ages crammed inside Boston’s historic Old South Meeting House, the organizing site of the Boston Tea Party in 1773. “I don’t know what those founders and early patriots would think about what we’re up against today,” she said.

She urged the lunchtime audience, with an overflow crowd outside, to “reject the demagoguery, the bigotry that is being peddled by the Republican candidates.” In a poke at Donald J. Trump’s slogan, “Make America Great Again,” she declared, “America never stopped being great; we need to make it whole again.”

As she raced through a laundry list of topics, she fleetingly sought to distinguish herself from Mr. Sanders on some of his signature issues, like free college tuition.

“I do not want to ask you to pay taxes to send Donald Trump’s youngest son to college,” Mrs. Clinton declared, drawing cheers from the many millennials in the crowd. Her proposal for reducing college debt is to allow students to refinance their loans, just as people refinance mortgages.

She also noted that her unnamed opponent “voted against the Brady Bill five times, giving immunity to gun makers and sellers.” And at one point she said, “We are not a single-issue country, we are a country that is diverse.”

She closed out her speech by asking everyone to vote for her and to bring their friends to the polls as her anthem, “Fight Song,” blared over the speakers.