Top Democrats are circulating a poll showing that one of the House's most progressive members — Rep. Alexandria Ocasio-Cortez — has become a definitional face for the party with a crucial group of swing voters.

Why it matters: These Democrats are sounding the alarm that swing voters know and dislike socialism, warning it could cost them the House and the presidency. The poll is making the rounds of some of the most influential Democrats in America.

"If all voters hear about is AOC, it could put the [House] majority at risk," said a top Democrat who is involved in 2020 congressional races. "[S]he's getting all the news and defining everyone else’s races."

The poll — taken in May, before Speaker Pelosi's latest run-in with AOC and the three other liberal House freshmen known as "The Squad" — included 1,003 likely general-election voters who are white and have two years or less of college education.

These are the "white, non-college voters" who embraced Donald Trump in 2016 but are needed by Democrats in swing House districts.

"white, non-college voters" who embraced Donald Trump in 2016 but are needed by Democrats in swing House districts. The group that took the poll shared the results with Axios on the condition that it not be named, because the group has to work with all parts of the party.

The findings:

Ocasio-Cortez was recognized by 74% of voters in the poll; 22% had a favorable view.

was recognized by 74% of voters in the poll; 22% had a favorable view. Rep. Ilhan Omar of Minnesota — another member of The Squad — was recognized by 53% of the voters; 9% (not a typo) had a favorable view.

Socialism was viewed favorably by 18% of the voters and unfavorably by 69%.

Capitalism was 56% favorable; 32% unfavorable.

32% unfavorable. "Socialism is toxic to these voters," said the top Democrat.

Between the lines: Dems are performing better with these voters than in 2016 (although still not as well as in 2018). So party leaders will continue to try to define themselves around more mainstream members.

The other side: Three members of The Squad — Omar, Rep. Rashida Tlaib of Michigan and Rep. Ayanna Pressley of Massachusetts — defended their approach while appearing in Philadelphia yesterday on a panel at the annual Netroots Nation conference, AP's Juana Summers reports:

"We never need to ask for permission or wait for an invitation to lead," Omar said, adding later that there's a "constant struggle oftentimes with people who have power about sharing that power."

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