It is good to have extreme voices, left and right, in Congress. It is even good to listen to them now and again. But you should never give them power over you. Especially since some of the far right view the Democrats as their opponents but the likes of McCarthy as their enemy.
Obviously the budget hardliners already have power over McCarthy.
Or he would be Speaker.
The overriding issue,though, is spending.
McCarthy is not trusted to hold the line on spending.
The way Congress works is to authorize spending, then appropriate money for those authorized expenditures, and then to authorize the Treasury Department to issue debt in order to pay for that appropriated money.
Raising the debt ceiling has been done 78 times in the last 60 years and it does not relate to which party is in power. Congress has always found a way to avoid a world financial crisis with band aids, etc., each time.
This faction , now that the GOP controls the House, wants to change business as usual, a debate the democrats avoided with its lockstep reaction to leadership orders.
It is most likely not going to be resolved until the stock market crashes and the kids in Congress have to grow up.