Sen. Bernie Sanders (I-Vt.) pauses during a political rally in Madison, Wis., on Wednesday. (Michael P. King/Wisconsin State Journal via AP)

Addressing yet another really big crowd -- this one in Portland, Maine, estimated at more than 7,500 people -- Sen. Bernie Sanders offered his own answer Monday as to why he's become such a draw on the presidential campaign trail.

"The answer, I think, is pretty obvious," the independent senator from Vermont told his overflow audience. "From Maine to California ... the American people understand that establishment politics and establishment economics are not working for the middle class."

It was a not-so-subtle jab at Hillary Rodham Clinton, the frontrunner for the Democratic nomination, coming from a self-described democratic socialist who's seen his crowds swell and poll numbers jump in recent weeks. Though few in Washington give Sanders much chance of winning the nomination, the rumpled 73-year-old is increasingly being seen as a real threat to Clinton.

[In Bernie Sanders, an unlikely — but real — threat to Hillary Clinton]

In an hour-long address that was streamed live on Sanders's Web site, he promised his audience that he would bring about "real change" if elected president. That includes raising the minimum wage to $15 an hour, making college tuition-free and guaranteeing workers family leave, vacation time and paid sick time. And it would mean higher taxes for corporations and the wealthy.

Aides to Sanders said the crowd Monday night at Cross Insurance Arena was more than 7,500 people, citing a figure from the facility manager. In recent weeks, Sanders has drawn 10,000 people to Madison, Wis.; more than 5,000 to Denver, and about 3,000 to Minneapolis.

On Friday, he also attracted more than 2,500 people to Council Bluffs, Iowa -- record turnout so far for the 2016 cycle in the nation's first presidential caucus state. (A chunk of the Council Bluffs audience came from just across the river in Omaha, Neb.)

[Sanders draws more than 2,500 to Iowa stop — tops for this presidential cycle so far]

Though Sanders has generated many of his largest audiences in states without early nominating contests, the size of those crowds is contributing to the buzz in places like Iowa and New Hampshire and has seemingly helped his fundraising efforts.