I don't bother with the right-wing propaganda networks so I don't know, but I can't imagine how they might spin this to blame Biden when his administration hasn't even been involved in the process.
The whole thing hinges on a purely internal conflict not just within Congress, but in the House specifically. How does that even colorably come to be blamed on an entirely separate branch?
I don't doubt that the propaganda outlets and the grifters will simply lie, and conjure up some entirely different account of things that won't match up at all with the plain objective reality of the whole thing stalling because a group of hard right House members are demanding concessions and refusing to vote in favor of a budget that doesn't include them, but I can't even imagine what it will be, since it will have to be essentially completely false, from start to finish.
Unfortunately, I also don't doubt that some significant part of the Republican base will believe whatever it is, since they've been so thoroughly indoctrinated and made so subject to their emotions that they literally can no longer distinguish between reality and fantasy.
Still though, even with as confused and misled and blinded by emotion as much of the Republican base is, and as brazenly dishonest as the propagandists and grifters that are profiting off of them are, I can't imagine how it might be the case that Biden will get the blame for this. It's not just that it's not narrowly true, but that there isn't even a colorable basis, as far as I can see, to even pretend that it is.
Statelessness is held to be necessary because, in the simplest terms, power corrupts.
If we institutionalize authority - if we create a structure in which authority is vested and positions within that structure that are held by specific individuals - then sooner or later (and history has shown that with communism it's generally sooner) self-serving fuckwads will capture those positions, then bend them to serve their own interests and the interests of their cronies and patrons, to the detriment of everyone else.
And yes - there are practical problems with not having institutionalized authority.
But the thinking of those who advocate for statelessness is that those problems can be, and would be, solved if people had the opportunity. But first we have to get the self-serving fuckwads out of the way, and the only way to do that is to not have institutionalized authority in the first place.