If a majority of the house wants the bill to come to a vote, how exactly can Johnson prevent the bill from doing so?
He can't. The House has a procedure called a discharge petition, which enables a simple majority to "discharge" any bill from any committee and force a floor vote on it.
Normally, this is not done, because the whole point of the committee process is to enable party leadership (especially the Speaker) to control the flow of legislation. If the majority wants something to pass, that would usually imply that the majority's party leadership wants it to pass, and also that the folks on the Rules Committee would want it to pass. However, we live in unusual times, so now there are at least three distinct groups who have some role in this:
- Johnson (the Speaker), who has the ability to do things like call a vote on suspension of the rules. This requires a 2/3 supermajority, but that supermajority itself functions as a convenient excuse (i.e. "this is bipartisan legislation with strong support on both sides, and putting it through the usual red tape would've been a waste of time"), which may even have the virtue of being true in some cases.
- The Rules Committee, which is usually stacked with the Speaker's close allies, is instead controlled in part by Republican hardliners. This Committee controls the regular scheduling of bills and the overall legislative calendar. Its "normal" function is to insulate the Speaker from being held directly responsible for scheduling decisions, as well as to relieve him of the administrative burden. Its alternative use by a faction of the party against the Speaker's preferences is atypical.
- The rest of the Republican conference, which is split between moderates and hardliners. Actually, if you look more closely, there are probably more than just two factions there, but the point is that usually, the conference as a whole follows the Speaker's lead. While, in principle, they can sign a discharge petition (which will also be supported by the minority, in most cases), most of the time, they prefer to let the Speaker and Rules Committee set the calendar as a matter of party discipline and unity, so discharge petitions are rarely successful in practice, especially since the names of all the signatories are immediately public, regardless of whether the petition succeeds or fails.
With such a thin majority, and such a sharp divide between factions, discharge petitions would appear to be more possible now than they have been in the past (but we still have not seen any successful petitions in this legislative session). However, it should be emphasized that signing a discharge petition is a public act of defiance against party leadership. It will be seen very harshly by the hardline wing of the party, and even the moderate wing doesn't particularly like discharge petitions either.