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Martin O’Malley’s call for more Democratic presidential debates at the party’s summer meeting last week may have been the loudest, but it was neither the first nor the last.

A growing number of party activists, from New Hampshire to Iowa, are voicing concern about the Democratic National Committee’s plan to hold six debates over all, with only four coming before the first four states finish voting. The party fears a lower number will of debates will diminish its ability to drive the discussion as the Republican contest, led by Donald J. Trump, dominates the news, and that a flabby process will leave the ultimate nominee unprepared for the general election.

The timing of the New Hampshire debate, sandwiched between the Hanukkah and Christmas holidays, has particularly rankled activists in the state, who have openly protested the decision.

Martha Fuller Clark, a state senator in New Hampshire who is not yet backing a candidate, said that she approached the party chairwoman, Representative Debbie Wasserman Schultz of Florida, at the meeting in Minnesota last week and expressed her disappointment.

“She seemed unwilling to consider a revision of the schedule,” Ms. Fuller Clark said. “She just said that whatever schedule she put out, people would be unhappy with.”

“If there isn’t an opportunity for lots of debates and consideration, it’s just really, I think, making it much more difficult” for the candidates to reach voters before the voting begins, she said.

Many activists have argued that the decision to abbreviate the debate schedule was done to benefit Hillary Rodham Clinton, the front-runner in most polls for the nomination.

Former State Senator Burt Cohen, who is supporting Senator Bernie Sanders of Vermont, accused Ms. Wasserman Schultz of “putting her finger on the scale” to help Mrs. Clinton.

“Debbie Wasserman Schultz has to schedule more debates and do it with more sensitivity to the primary schedule,” he said, adding that if she did not, she should consider leaving her post, a comment he later tried to play down, saying it was premature to suggest such a thing.

A spokeswoman for the national party declined to comment. But party officials have insisted they were trying to bring as much voter interaction through forums and other means as possible, and suggested they began looking toward the Republican Party’s efforts to control its own debate process as far back as January. Ms. Wasserman Schultz has strenuously objected in private conversations to claims she tried to help Mrs. Clinton.

Still, in past cycles, there were many more debates, including unsanctioned debates, and they began earlier. But in 2004 and 2008, there were no penalties for taking part in the unsanctioned debates, which made up the majority of them in those years. This cycle, David Mercer, a former party official, noted, candidates who take part in unsanctioned debates risk being barred from the official forums.

Some Democratic activists point out that all of the Republican candidates, including those complaining now, agreed to the sanctions that were ultimately put in place.

Still, during the spring of negotiations between the party committee and the campaigns, the Clinton campaign had pushed for a lower number on the debate spectrum, while Mr. O’Malley’s campaign had called for many more.

When Mr. O’Malley, the former Maryland governor who has been struggling to gain traction in the polls, but trying to position himself as the best alternative to Mrs. Clinton, used his speech at the summer meeting to condemn the party, he was met with cheers. Many high-ranking party activists have privately shared their concerns over the debate schedule, complaining that the criticisms risk getting amplified on places like MSNBC’s “Morning Joe” program.

A spokeswoman for Mrs. Clinton declined to comment. But even some of her supporters are encouraging a change in the schedule.

“I’m very supportive of the more the merrier in terms of debate,” said State Senator Lou D’Allesandro of New Hampshire, a Clinton supporter. “It’s a stage that’s ready-made for her. Why limit anything in this business? That’s not the American way.”

Sandy Opstvedt, an uncommitted party committee member from Iowa, said she also wants to make her voice heard to Ms. Wasserman Schultz.

“I think the debates actually help the candidates, and they just become more adept at debating,” said Mrs. Opstvedt, who, like Mr. O’Malley, described it as an opportunity to showcase the party’s ideas.

Donna Brazile, a national party vice chairwoman, said that she could understand the perspective from both sides.

But she also noted that there’s the possibility of another candidate joining the race: Vice President Joseph R. Biden Jr.

His presence “might turn all of this upside-down,” she said. “Starting out with six is productive, but it could grow.”