@Virginicus - the Freedom Caucus certainly will. However, the realpolitik of the situation is that any Speaker will need Democratic support to get elected at this point.
There are three possible outcomes here:
The Republicans are able to control their caucus and elect a new speaker entirely with GOP votes (highly unlikely, and if they do, a new leader will be just as vulnerable as McCarthy was until 2024)
The Republicans are able to peel off enough Democratic votes to get a new speaker in by advancing a moderate and granting concessions (possible, but this effort would likely lose as many GOP votes as it would gain Dem ones unless they convince Jeffries to rally his caucus in support of a moderate)
The Democrats are able to peel off enough GOP votes to elect Jeffries (slightly less likely than 2, above) - this is the worst possible scenario for the GOP
Jeffries has them over a barrel as long as he maintains caucus discipline. Thus far he's doing a far better job at it than the GOP, plus he's still got Pelosi's connections in his back pocket (and she's definitely not about concessions to the GOP at this point). This opinion piece is both an olive branch and a subtle threat to those on the GOP side who can still do basic math - it's "work with us, or watch us take the Speakership before 2024".