The new Republican strategy for this whole thing is to make the Ds and President Obama the party of NO. They plan to force as many hard votes with the mini CRs as they can and hope that the visuals will help them and give them red meat for future political adds. Reid has hold firm in either voting out this bills or not bringing them to the floor, but I think there is a better strategy.
I think all Ds should vote in favor of those bills in the house. Once they reach the Senate Harry Reid should pick them and modify them them to have the spending for those areas back to pre sequester levels, even more if you want to make it harder. Then bring them to the floor and let Cruz and company try to filibuster them, or once they pass the Senate ping pong them with the house so they either accept the presequester level of expending or turn down the bills.
I think this will be a win either way. I know there is a reason to want the whole thing to be passed as a whole but because this are all short mini CRs they will be put into one once the Republicans fold.