A movement that actually believed that reducing federal spending was extremely important would, it seems to me, be quite willing to make concessions in order to obtain large quantities of spending cuts. Viewed in that light, it’s not obvious to me that backing away from a $4 trillion deal primarily composed of spending cuts constitutes a “more conservative” option than saying yes. You’re seeing that very little has changed in practice from the Bush years, when the GOP agenda consisted of aggressive tax cutting made palatable by refusing to pair the cuts with spending reductions. Now, ostensibly, cutting spending is the order of the day. But the bargaining strategy is entirely built around a tax-focused goal rather than a spending-focused one.
This is because they only care about tax cuts for rich people. A few members might have some idiosyncratic spending concerns, such as "we're too generous to poor people," but basically they just care about tax rates on rich people. That's it.