Advisers to Ms. Warren defended her campaign finance decisions and noted that big-money fund-raisers , like the ones with Mr. Connors and Mr. Rendell, accounted for only about one-quarter of the $25.8 million she raised in 2017 and 2018.

Kristen Orthman, Ms. Warren’s communications director, said the senator “believes that to take back the White House we need to build a grass-roots movement.”

“When we made the decision to run the campaign this way, the players in the usual money-for-influence game dismissed it as naïve and said it would never work and it would kill the campaign,” Ms. Orthman said. “We’re pleased that our grass-roots strategy has been so effective that they’re now threatened enough to be attacking us for it.”

Since Ms. Warren’s announcement in February, her disavowal of closed-door events with the donor class has become an inextricable part of the DNA of her candidacy as she promises to bring about structural change to American society.

It is the reason, her campaign advisers say , that she has the time to dedicate to hourslong selfie lines, to expand the map of states she can visit, and to call up small donors at random to thank them for giving, rather than pleading for more $2,800 donations from the well-to-do.

“The best president money can’t buy,” read campaign T-shirts and tank tops.

That message — paired with a raft of ambitious policy proposals — resonated with enough small contributors to propel Ms. Warren to raise $19.2 million in the second quarter of 2019 (the third most in the field) and to the top tier in the polls.

The only other Democratic candidate to bypass big-money events is her fellow liberal in the race, Senator Bernie Sanders. He has transferred $10.1 million from old accounts to his 2020 campaign, but, unlike Ms. Warren, he had eschewed high-dollar fund-raisers in past races. (Other senators transferred money into their 2020 bids as well.)