Taken together, such hardball tactics suggest that emboldened progressives intend to tap into the populist energy coursing through the Democratic Party to ensure that their elected officials hold to the liberal line.

“Given that we are a vast majority of the party’s voters, and represent many of the party’s financial contributors, to see that level of disrespect shown to Elizabeth Warren’s message, you know, we needed to answer fire with fire,” said Mike Lux, a longtime liberal strategist.

By directly going after Ms. Warren, who has an avid following among progressives, Third Way all but ensured that it would get the fight it seemed to want to pick.

While she has repeatedly said she will not run for president, Ms. Warren is seen by many on the left as the candidate who could stop Hillary Rodham Clinton from claiming the Democratic nomination in 2016. And even if Ms. Warren does not run, progressives want to use this period to send a message to Mrs. Clinton that the Democratic Party is now more unabashedly liberal than it was when her husband was elected president in 1992.

Liberals have witnessed the success the right has enjoyed in recent years by using such tough tactics. Conservative groups have pushed Republicans to take a harder line, most recently over the federal health care law, and have seen their leverage with officeholders grow.

“They have been much tougher on their moderates than we have historically,” Mr. Lux said, “and it shows in terms of the policy debate as the Republicans keep moving to the right and our guys keeping getting mushier.”

Asked about the criticism, a Third Way official cited similar efforts by the right.

“We hope that the Democratic tent remains big enough for a serious policy debate and that we don’t begin to drive out those we don’t agree with, like the Republicans have done,” said Matt Bennett, a founder of the group and its vice president for public affairs.

As for the group’s financing, Mr. Bennett said that only “three-tenths of 1 percent” of the annual budget comes from the banks Ms. Warren addressed in her letter.