“Our process has resulted in more women and candidates of color participating in our primary debates than billionaires,” said Xochitl Hinojosa, a committee spokeswoman. “No one who has failed to reach 4 percent at this point in the race has ever gone on to be the nominee. Our debate criteria reflects this.”

Leah D. Daughtry, a longtime Democratic National Committee member who sits on the party’s rules committee, said she’s had a number of conversations in recent days with other members about how to change the system to include more candidates of color. No one has come up with a workable solution.

“I don’t know how you fix it now without upsetting the apple cart,” she said. “But it’s a problem. It’s a real problem.”

Some prominent Democrats say the party cannot be blamed for the failure of candidates of color to make the stage, placing responsibility on their inability to build momentum for their efforts — particularly among black and Latino voters.

A growing number of voters, especially younger black voters, have rejected the notion that mere representation equals the kind of change the Democratic base is hungry for. Polls have consistently shown the former vice president Joseph R. Biden Jr. leading among African-American voters, while Senator Bernie Sanders of Vermont is widely popular among Latinos.

“When people make the case that the standards and requirements should be lowered so that candidates of color can make the debate, as a Latina, I find that insulting,” said Maria Cardona, a former D.N.C. official. “The reason why the candidates right now are the ones at the top of the polls are because these are the candidates who are getting the majority of support from, guess who, voters of color.”

Some party officials dismiss the criticism of the debate criteria. Ms. Harris, they note, had qualified for the December debate but chose instead to drop out, they said.