The Democratic National Committee (DNC) appears poised to dramatically reduce the influence of superdelegates on the party's presidential nominating process despite vocal criticism from House Democrats.

CNN and Politico report that DNC Chairman Tom Perez Thomas Edward PerezClinton’s top five vice presidential picks Government social programs: Triumph of hope over evidence Labor’s 'wasteful spending and mismanagement” at Workers’ Comp MORE has thrown his support behind a plan floated by American Federation of Teachers President Randi Weingarten that would deny superdelegates a vote on the first ballot of the party's presidential nominating process, while allowing them to vote on subsequent ballots and proposed rule changes.

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The plan would likely strip superdelegates of their votes in all but a few cases, as the party rarely moves to a second ballot in the nominating process.

This week, Perez met with several Democratic members of Congress, including Reps. David Price David Eugene PriceHouse panel approves measure requiring masks on public transport Overnight Energy: 350 facilities skip reporting water pollution | Panel votes to block Trump's 'secret science' rule | Court upholds regulation boosting electric grid storage Committee votes to block Trump's 'secret science' EPA rule MORE (N.C.), Grace Meng Grace MengHouse passes resolution condemning anti-Asian discrimination relating to coronavirus Clark rolls out endorsements in assistant Speaker race This week: House returns for pre-election sprint MORE (N.Y.), Gregory Meeks Gregory Weldon MeeksBottom line Democrats go big on diversity with new House recruits Chamber of Commerce, banking industry groups call on Senate to pass corporate diversity bill MORE (N.Y.) and Rosa DeLauro Rosa Luisa DeLauroOvernight Health Care: CDC pulls revised guidance on coronavirus | Government watchdog finds supply shortages are harming US response | As virus pummels US, Europe sees its own spike Trump HHS official faces firestorm after attacks on scientists Ahead of a coronavirus vaccine, Mexico's drug pricing to have far-reaching impacts on Americans MORE (Conn.), who pushed back against the proposal while offering their own.

However, the lawmakers' proposal was rejected due to it not meeting the Unity and Reform Commission's earlier decision to reduce the number of unpledged delegates by two-thirds, CNN reports.

Reducing the influence of superdelegates has been a charged issue for the party, supported largely by labor activists and backers of Sen. Bernie Sanders Bernie SandersOutrage erupts over Breonna Taylor grand jury ruling Dimon: Wealth tax 'almost impossible to do' Grand jury charges no officers in Breonna Taylor death MORE (I-Vt.). The party will vote on the proposals in August.

The Unity and Reform Commission, which was formed following the heated 2016 Democratic presidential primary, voted earlier this year to both reduce the number and role of these delegates at the party's conventions, which CNN reports could result in some members of Congress losing their status as superdelegates.

Still, House Democrats said they felt "heard" by Perez during the meeting and expressed interest in the possibility of a compromise.

“I was able to talk about some ways the twin objectives could be achieved: to significantly reduce the number of unpledged delegates, and secondly, to do that without denying or overriding anyone’s vote at the convention,” Price told Politico.

A statement from Perez's press secretary said that the DNC would ensure that any proposal adopted by the DNC would "significantly" reduce the role of unpledged delegates at the convention.

“The DNC heard concerns that members of Congress had with the current consensus and discussed how any proposal must significantly reduce the role of unpledged delegates, a commitment that the full DNC voted for in March,” DNC press secretary Michael Tyler told Politico in a statement.

“We'll continue to seek input from members of Congress who are integral to our efforts to strengthen the Democratic Party and ensure that our 2020 nominee sprints out of the gates ready to defeat Donald Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE.“