One problem. There's no poll that supports defunding Obamacare. Obama knows it. That's why he will veto any attempt to do it.
Any other ideas?
Ahh, and there are polls showing overwhelming support for it?
Furthermore, getting him to veto any attempt to fund the government that does not include funding for Obastardcare is precisely the point - if the republicans keep offering up proposals to fund the various "important" - but not "essential" - parts of the federal government and Obama keeps knocking them down, then it becomes quite clear that the only obstructionist in the room is Obama, not the republicans; it becomes obvious that the only person denying Americans their personal pet "bennies" from the federal government is Obama, not the republicans. That shifts the blame for the shutdown to Obama and the democrats or, more precisely, it lets them take ownership of the shutdown all by themselves.
In other words, getting Obastard to veto any appropriations bill for any part of the federal leviathan that does not include funding for Obastardcare is part of the point of this exercise, not a lamentable mistake from this exercise.
And that involves more than just some misbegotten focus on "NOW;" it involves framing the discussion for 2014 and beyond and attempting to set the terms of debate by letting the democrats prove themselves to be the hyper-partisan obstructionists.