(CNN) -- Democratic members of Congress are starting to accept that they may lose parts, if not all, of their status as superdelegates to the Democratic National Convention in 2020 when the party votes for its nominee for president.
Reps. David Price, Gregory Meeks, Rosa DeLauro and Grace Meng -- a Democratic National Committee vice chair -- met Wednesday with Chairman Tom Perez, American Federation of Teachers President Randi Weingarten and Lee Saunders, president of the American Federation of State, County and Municipal Employees, to discuss the superdelegate proposals required to be passed by the end of the month.
Congressional Democrats -- all of whom are designated superdelegates, automatic unleashed delegates who can vote for any nominee -- have been meeting with Perez about proposals to strip away that status for the 2020 convention. Other superdelegates include former Democratic presidents, governors, senators and DNC members.
During a meeting with Perez last week, many members were angry about proposals to rid the party of superdelegates completely.
According to a source with knowledge of the meeting, members of Congress want to maintain their status but "understand the political dynamics at play."
Grass-roots activists have been working to get the DNC to eliminate superdelegates, claiming such delegates gave Hillary Clinton an advantage over her fellow candidates, like Sen. Bernie Sanders, during the 2016 primary process. A unity commission was formed to propose changes for the DNC Rules and Bylaws Committee to pass by the end of this month.
At Wednesday's meeting, first reported by Politico, the members felt "heard" and seemed to be more pliable to the changes, according to the source.
"We had a good, open discussion in which we were able to voice our views and have them taken seriously," Rep. Rosa DeLauro said in a statement to CNN.
Relations between the DNC and members of Congress that had frayed over the plan to curb the influence of superdelegates in the presidential nomination process are getting better, a source with knowledge of the negotiations tells CNN, but disagreements persist.
"Yesterday's meeting was a constructive effort, and nobody wants a fight on this, but the idea that we're at or near consensus as some have suggested, is definitely a stretch," the source said.
They added that while this meeting was better than previous, more contentious, affairs, the issues "were not resolved."
Rep. David Price, in an interview with CNN on Thursday, said the disagreements between the DNC and members of Congress were "a work in progress," but that their latest meeting was "cordial" and "informative."
"The ball is in their court, not ours," said Price, who was brought in because he was the executive director of the Hunt Commission that re-evaluated the Democratic nomination process after the 1980 election that led to the creation of superdelegates.
Price said "several" proposals were floated at the Tuesday meeting, but that one of the key concerns from the members of Congress was the idea that they would have to run against their own constituents to be a delegate to the DNC if they lose their current status. He added that he believes it is possible to reduce the number of unpledged delegates but not deny them their vote in the process.
He declined to get into those specifics.
"This is not about one class of delegates versus another, it is about how do you have inclusive convention that includes everyone that needs to be there," he said. "I would say that is more for the party's benefit than anyone else.
And Meng, who also serves as a DNC Vice Chair, said in a statement that she feels she has a unique role "making sure that the DNC is listening to the concerns that House Democrats have with the current proposal" and ensuring that "the DNC is listening to the concerns of activists and organizations to ensure that their voices are heard as well."
She declined to comment on any of the plans "until the Rules and Bylaws Committee is finished" with its work.
Rules committee members met in Rhode Island last Friday to discuss new proposals. Weingarten, a member of the committee, proposed keeping some superdelegates with all rights except voting for the party's nominee on the first ballot at their convention. The "third way" plan (as it was called) was supported by Perez.
Some committee members, including many who represent minority communities, argued excluding superdelegates on the first ballot was tantamount to voter disenfranchisement. As a compromise, members seemed to agree in principle with Minnesota DFL Chairman Ken Martin's proposal to find a way to keep superdelegates on the first ballot so long as they don't affect the outcome of the vote -- known as the "third way plus" plan.
Both plans were discussed at Wednesday's meeting. Only one plan was proposed by the members, according to the source, but it did not conform with the unity commission's requirements to reduce the number of superdelegates by two-thirds.
Rules committee members will vote on a final proposal by the end of the month, which will need a full DNC vote at its August meeting in Chicago.
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