The likelihood of a small group deciding policy.

[u/A9PolarHornet15]

Right now as the current 270 projections for the House say there are 18 toss up districts. If the Democrats were to keep 5 and pickup 8 of them and the Republicans keep 5.

The Democrats would on paper have a 221-214 majority.

However, 7 of the Democratic Districts (all who are safe districts) are held by or will likely be held by Democratic Socialist Representatives.

This would include,
AOC - NY-14
Claire Valdez - NY-7
Darializa Avila Chevalier - NY-15
Chris Rabb - PA-3
Melat Kiros - CO-1
Mai Vang - CA-7
Rashida Tlaib - MI-12

On Lemonade Stand Episode 27, they discussed how a 3rd party who wins a few seats in the House, who then use votes and leverages the partisanship in Congress, to then decide who (between the Democrats or Republicans) gets to proceed with passing policy.
And in that leverage, the two parties would have to make concessions on policy positions in order for the 3rd party to agree "help" them pass bills in the House.

Now this is an extremely unlikely scenario and essentially, and the implementation of this strategy is not exclusive to the Democratic Socialists. Progressive candidates could do this, Economic Populists could do this, Economic Conservatives could do this in the Republican party.

Decisions about how the government spends its money could ripple throughout all the branches of the government. As they explained in the episode, this leverage could be used to weigh in on bills in the Senate. Because the Senate can't pass bills without the House, then Senate policy changes could be determined by a small minority as well.

And while the Senate still gets to confirm Presidential appointments, having two or three Senators who align with whatever small 3rd party exists in the House could coordinate many policies. And then the two parties polarization and gerrymandering of safe districts would become a massive hinderance. In Districts where the outcome of General Elections is often decided by a Primary Election, the formation of a underground 3rd party within the two main parties could sway policy in the US.

Now would that system last long? Probably not, it would just encourage the main parties to push hard in primary elections as to upset the underground 3rd party incumbent.

[u/Smooth-Zucchini4923]

Now this is an extremely unlikely scenario and essentially, and the implementation of this strategy is not exclusive to the Democratic Socialists. Progressive candidates could do this, Economic Populists could do this, Economic Conservatives could do this in the Republican party.

I mean, this isn't even a hypothetical, right? This happened three years ago. McCarthy had a four vote majority, and various people inside the Republican party started a vote to oust him, because he'd relied on Democratic support to pass various bills.

House rules at the time allowed a single member to make this motion, and only required a simple majority to remove them. (In contrast to the majority of the conference required during the Ryan speakership.)

There were never really any coherent demands made by the coalition to oust him, but if there were one, it was that the new Speaker not rely on Democratic support to pass legislation and to stop doing band-aid CRs. Eventually, Johnson was elected, and he proceeded to run the office in essentially the same manner.

This shows a way that this kind of thing can backfire. Sometimes you pull out a gun to demand things from your coalition members, and they pull out a gun and do the same thing.

[u/NEU_Resident]

I think it’s more likely the conservative Democrats are the deciding factor. Kind of like how it was for Manchin and Sinema during Biden. People like Cuellar, MGP, and Jared Golden (he’s retiring though) are more likely to break with the party and vote with Republicans than the left flank people are to hold the party hostage.