(CNN) Following Vermont Sen. Bernie Sanders' victory in Tuesday's New Hampshire primary , some of the most vulnerable House Democrats are expressing significant unease at the prospect of sharing a national ticket with an avowed democratic socialist.

"I think it would have some significant down-ballot effects, and what I tell everybody is he may well win the popular vote," freshman Democratic Rep. Dean Phillips of Minnesota told CNN's Manu Raju on Thursday. "In fact, I wouldn't doubt that. But the five or six states that are going to matter in the Electoral College makes it a real question mark in maintaining the House of Representatives. There are probably 25-30 seats that absolutely would be impacted directly by having a self-avowed socialist at the top of the ticket. And I say that ... you know ... he's not a Democrat, you know, and that's something that I wish was better understood."

Whoa.

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Phillips' comments echo similar remarks made by Democratic Rep. Joe Cunningham of South Carolina in the Charleston Post and Courier on Wednesday.

"South Carolinians don't want socialism," Cunningham told the paper. "We want to know how you are going to get things done and how you are going to pay for them. Bernie's proposals to raise taxes on almost everyone is not something the Lowcountry wants and not something I'd ever support." Asked whether he would vote for Sanders if the senator wound up as the party's presidential nominee, Cunningham replied: "Bernie Sanders will not be the nominee."

Double whoa.

Here's why Democrats can't -- and shouldn't -- ignore the concerns of the likes of Phillips and Cunningham. They both sit in districts that will be heavily targeted by Republicans in November. Phillips defeated Republican Rep. Erik Paulsen convincingly in 2018 in a suburban Twin Cities seat that Hillary Clinton won by 9 points in 2016 but that President Barack Obama had carried by only a single point four years earlier. Cunningham won the Charleston-based South Carolina seat previously held by Republican Rep. Mark Sanford; Trump won his district by 14 points in 2016.

That these majority-maker Democrats are already willing to speak publicly about their belief that Sanders could cost the party the House speaks to the level of concern his ongoing rise is creating among those who would have to share the ballot with the senator from Vermont. (We now rank Sanders as the most likely Democratic nominee .)

House Speaker Nancy Pelosi has, to date, offered next-to-no thought about her party's presidential race generally or the rise of Sanders particularly. But her views on the danger to the House majority of fully embracing the views of the most liberal voices within the party are well-known.

Pelosi publicly clashed last year with Rep. Alexandria Ocasio-Cortez of New York, a prominent Sanders backer. Speaking of Ocasio-Cortez and her so-called "Squad" of freshman female lawmakers, Pelosi told The New York Times' Maureen Dowd : "All these people have their public whatever and their Twitter world. But they didn't have any following. They're four people and that's how many votes they got." (Of the "Squad," Ocasio-Cortez as well as Rep. Rashida Tlaib of Michigan and Minnesota's Rep. Ilhan Omar are supporting Sanders. Massachusetts' Rep. Ayanna Pressley is backing Sen. Elizabeth Warren of Massachusetts.)

A few months prior to that comment, Pelosi said this of the Squad: "While there are people who have a large number of Twitter followers, what's important is that we have large numbers of votes on the floor of the House."

Pelosi has been vigilant in seeking to remind her caucus not to assume that the politics of their particular districts are the politics of the country -- or the solution to Democrats' return to the White House. "What works in San Francisco does not necessarily work in Michigan, " Pelosi told Bloomberg News in an interview last fall. "Remember November. You must win the Electoral College."

At the presidential level, former Vice President Joe Biden has sought to make many of the same points that Cunningham and Phillips are articulating. Here's Biden from last Friday's debate in New Hampshire

"We're going to not only have to win this time, we have to bring along the United States Senate. And Bernie's labeled himself, not me, a democratic socialist. I think that's the label that the President's going to lay on everyone running with Bernie, if he's a nominee. ....

"As you all look at it up here in New Hampshire and around the world -- excuse me, around the country -- you have to ask yourself, 'Who is most likely to help get a senator elected in North Carolina, Georgia? Who can win Florida, Pennsylvania, Minnesota? Who can do that?' "

My strong sense is that Cunningham and Phillips are just the tip of the spear when it comes to concerns among swing-district Democrats about what Sanders leading the Democratic ticket would mean. And if Sanders wins the Nevada caucuses on February 22 -- as he is favored to do -- you may well start hearing from a lot more of those skittish Democratic House members.