It's Congress' obligation to control the purse strings of government. They could fund the armed forces and border security, then prioritize other programs accordingly, with the great monstrosity, Obamacare, being last, and effectively shut out for funding.
I think that many, if not most, other programs should experience scaled-down funding also. But, if there's a (OMG!) government shut-down, let it be that part (or those parts) that are least palatable and most onerous.
the cost of the political capital is extreme, is just a head-fake. Because, the decision to either accept the budget without OBC funding or "shut down government" would fall to the Oval Office. It's a win/win for Republicans this way, unless you're a big-government Republican.
The folks who want to keep it "funded" are those that also want to tinker with it, and keep Washington DC's thumb on it. Why?