Sen. Elizabeth Warren pushed her pledge to have her presidential campaign avoid big-money donors a step further this week, committing to avoid pricey fundraisers even if she is elected the Democratic nominee.

"I'm not going to do the big-dollar fundraisers. I'm just not going to do it. The whole notion behind this campaign is that we build this together. And that's exactly what we're doing," the Massachusetts progressive told CBS News in an interview published on Tuesday.

The interview came as Warren surged past former Vice President Joe Biden in several national polls, becoming the front-runner in an average maintained by Real Clear Politics.

Read more: Wall Street Democrats warn the party: We'll sit out, or back Trump, if you nominate Warren

Warren raised $24.6 million in her most recent fundraising quarter, the campaign has said, well ahead of Biden and just a hair behind progressive rival Sen. Bernie Sanders.

Warren has stayed away from big-dollar fundraisers in the primary, instead collecting her millions from a vast network of online supporters. She had not previously said she would avoid big-dollar fundraisers during the general election if made the nominee.

In an interview with MSNBC's Chris Hayes earlier this year, Warren signaled that her pledge to avoid big-dollar fundraisers didn't apply in a general election.

"I'm just going to be blunt. I do not believe in unilateral disarmament. We got to go into these fights, and we got to be willing to win these fights," she said at the time.

Warren's communications director, Kristen Orthman, confirmed she will not be taking part in big money fundraisers in the general election and will continue to not accept help from political action committees.

"When Elizabeth is the Democratic nominee for president, she's not going to change a thing in how she runs her campaign," she said. "No special access or call time with rich donors or big dollar fundraisers to underwrite our campaign."

The new commitment is significant because it could put Warren at a financial disadvantage against President Donald Trump, whose reelection campaign is already spending millions of dollars per week on advertisements. Trump and the Republican National Committee raised $125 million last quarter.

Rufus Gifford, President Barack Obama's fundraising chief during his 2012 reelection campaign, said on Twitter that Warren's move could hurt the rest of the Democratic Party's fundraising efforts next year.

"A Presidential nominee is not just responsible for fundraising for his/her campaign," Gifford wrote in a tweet. "They are the de-facto head of the Democratic Party and for all 50 State Parties."

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A senior Wall Street Democrat, who has not committed to a nominee, told CNBC on Wednesday that Warren's decision to forgo big money against the fundraising juggernaut of Trump could destroy the party's chances of winning back the White House.

"It's totally stupid because she should take the money," the banking executive said on the condition of anonymity in order to speak frankly about the situation. "She should take money from any legal source that doesn't compromise her ethical beliefs. We are going to be outspent 2-to-1 if she does this."