The entire premise of shutting the government down over Obamacare is that shutting the government down is bad and has bad consequences. The consequences were supposed to be so bad that Democrats flinch from the horrors being inflicted on the American public and agree to repeal the Affordable Care Act. For that to work, two things need to be the case. The first is that middle-class people must suffer from the absence of government services. The second is that middle-class people must turn their rage against the uninsured and demand the repeal of Obamacare rather than turning their rage against Republicans.
The problem for Republicans is that the shutdown is clearly—obviously and unambiguously—their fault, so the public’s rage is much more likely to turn against them. The small-batch funding idea is supposed to tone that rage down. But absent the rage, there’s no leverage.