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Now, it's true that the antitax wing of the party suffered a defeat of its own a few months back when Republicans agreed to raise taxes as part of a deal to resolve the "fiscal cliff" (putting the sequester off for three more months). But it seems that battle has made them even more determined to win this time around.
At the same time, the relative diminution of the pro-defense wing of the party may have been inevitable – in part, because of the legacy of the Bush years. The GOP's defense hawks are now primarily associated with the unpopular war in Iraq and unpopular public figures like former Vice President Dick Cheney. In fact, frustration with the Bush administration's willingness to spend huge sums of public money on wars and other foreign interventions (as well as on new domestic spending, like the Medicare prescription drug plan) was a primary factor in the creation of the tea party.
The sequester itself may still be resolved at some point – if not before it officially hits next week, then perhaps in subsequent weeks as its effects begin to play out. But the impact of this particular battle on the internal dynamics of the Republican Party – particularly if it establishes the antitax wing as dominant above all others going forward – could be much longer-lasting.