DSA is not a political party. It's also not an arm of the Democratic Party. It's supposedly "non-partisan". They do endorse.
Blue Dog is considered an arm of the Democratic Party, but many are worried that they will "flip" or become "independent". (Manchin)
Here's something funny. We have three DSA candidates who serve on our city council. I consider them progressive Democrats. They're doing a great job..
However, last summer in three other districts, DSA endorsed three moderate Democrats in runoffs (our races are non-partisan) because their opponents were too conservative...LOL...I thought that was funny. Two of the moderates won, and unfortunately the other one, lost to the conservative. The chapter didn't endorse the moderates because they were progressive. (Well actually one was, but she was running in a red district, and knew how to work in GOP circles also. She was a great candidate, who unfortunately lost)
They endorsed them at the last minute because their opponents were bad...I thought it was funny.
There are pockets and places where they "work" and can "work" with Democrats. New York City for example. They work best with Dems in blue, more progessive areas. However, they don't poll well if they try to run in red districts. I know someone who although wasn't endorsed by DSA, was pretty much aligned with them. She ran against Chip Roy for congress and did not do very well. Afterward, she got involved in SDEC (State Democratic Executive Committee) and disaster relief for Kerrville etc, and she won at "At-large" seat on City Council in Kyle, TX (Austin suburb). At-large districts are harder for progessives to win, but she won!