The list of Republicans who publicly support a clean CR is now at 24, as Jennifer Bendery (who is doing a great job on this story) reports. That number has been stable for a while, but partially because four Members who were previously on the list have flipped.
As I said before, my sense of how this all plays politically is that somewhere between this list reaching 25 and reaching 60, it becomes a large enough problem for Republicans that their position likely collapses entirely, and a shutdown vote really does happen. Because of that, if the list is slowly increasing, Democrats get an additional incentive to hang tough (although, given the GOP position, that's not really all that hard anyway).
My best guess, however, is that we've seen the answer I asked earlier: will getting to a House majority make it easier for other Republicans to out themselves as clean CR supporters or will it make it harder? The answer sure seems to be: harder. There are probably two things going on. One is that as the shutdown goes on, positions held by partisans harden, which makes it harder to go against them. The other, however, is simple numbers. The eventual agreement needs at least 17 Republicans, but probably a bit more than that; those Republicans know who they are, and therefore they lose little by going public now. However, there are presumably a lot of Republicans who support ending this with a clean CR (and probably a clean debt limit increase also) but hope that they can get out without having to support it themselves.
That's probably, also, the best explanation for the four backsliders. It might be that leadership (or Tea Partiers) put pressure on, and they backed down. But a more likely answer is that they wanted the shutdown to end enough to go public, but once enough other clean CR Republicans were identified, they realized their votes were no longer needed.
The only problem with that is that it really does remove the pressure that they presumably wanted in the first place. If the list was 28 and climbing...well, it's a much larger threat than 24 and basically stable.
I'm still watching that list, but at this point I think it's unlikely that it's how the shutdown ends.