I've asked some Republicans sources to explain their thinking to me. But none of the answers quite seems to add up.
One answer is that they're hoping the sequester gives them so much leverage that the Democrats fold and accept an equivalent or larger package of spending cuts that Republicans prefer. But I can't find any Republicans who actually believe that will happen.
Another explanation is that Republicans don't want to cut tax deductions now -- which is the key to any deal with the Democrats -- because they want to use those deductions to pay for rate-lowering tax reform. But if they're not open to new revenues, they're not getting rate-lowering tax reform while President Obama remains in office. And if they take power after Obama leaves office, they can just lower tax rates without paying for it, as they've done many times before.
A third answer is that the anti-tax pledge holds that cutting deductions to reduce the deficit is a tax increase, and Republicans won't vote for a tax increase, even if it results in a policy outcome they vastly prefer. In other words, it's ratio-myopia.
And perhaps that's the real answer. But it's a bit hard to believe. Perhaps I'm missing something?