By Eric Bradner, CNN

(CNN) -- Vermont Independent Sen. Bernie Sanders never actually joined the Democratic Party -- and some party officials are still bothered by it.

Bob Mulholland, a Democratic National Committeeman from California, introduced a resolution that the party will consider at its Las Vegas meeting later this week calling on Sanders and Maine Independent Sen. Angus King -- both of whom caucus with the Democrats -- to actually join the party.

"There's only two real teams in the presidential election in 2020, and that's Trump versus a Democrat," Mulholland said Tuesday night. "And with Trump running the White House, we need more people to call themselves Democrats and stop standing on the sidelines."

Any DNC member can introduce a resolution -- and Mulholland's has a long way to go before having the party's endorsement. It'll head to a resolutions committee that will meet Friday in Las Vegas, where it could be amended, rejected or approved. It would then advance to the full DNC membership for a vote Saturday.

Even then, it would have no binding impact on Sanders and King.

In an interview with CNN's Wolf Blitzer on Tuesday, King said he won't join the Democratic Party.

"I've been an independent since the early '90s. I was a governor as an independent. That's who I am," King said.

"I caucus with the Democrats. You have to choose one caucus or the other," he said. "It's worked out. I more often vote with the Democrats, but not always. I like to call them as I see them, and that's where I'm going to stay."

Mulholland's resolution says that "the DNC recognizes the important contributions of the independent senators from Maine and Vermont to causes at the heart of the Democratic Party's mission and urge them to run as a Democrats."

It also says that "the DNC urges elected officials, candidates and voters who share common goals and beliefs with Democrats to register or affiliate with the Democratic party in 2017, 2018 and beyond."

Sanders' spokesman didn't respond to a question about the DNC resolution.

The Vermont senator has exerted his influence on the Democratic Party's platform, messaging and infrastructure, however.

The party's 2016 platform was the product of lengthy negotiations between the Sanders and Democratic nominee Hillary Clinton's camps. And House and Senate Democrats' 2018 platform is heavily influenced by Sanders' economics-focused, populist policy positions. Meanwhile, most of the Democratic senators seen as contenders for the 2020 presidential nomination co-sponsored Sanders' single-payer health care bill in September.

On Wednesday the DNC's unity commission, which includes members appointed by both Sanders and Clinton, is meeting to discuss changes to the party's rules and presidential nominating process.

Still, Sanders' outside political organization, Our Revolution, has feuded with the DNC -- including an episode over the summer in which tensions boiled over after DNC staffers brought water and doughnuts to Our Revolution members who were prevented by security from entering the building to deliver petitions and saw the snacks as a dismissive gesture.