How many times has this happened recently? Right before someone/some other party has the opportunity to do something they are legally allowed to do, their opposition changes that rule so they can't do it.
I'm not super savvy on stuff like this, but the jist of it is this (plz correct me if I'm in error...) - there is a rule in the House of Reps that states if there is a conflict over a bill that any House member has the right to request disposal. (So in this case, the disagreement - funding/shutdown) By the original rule, any House member can make a request, and that request is to re-open the government.
So what the GOP did (I'm not really sure how...) is make a last-minute amendment to that rule, on the day of the shutdown, that only the House majority leader may request it. Coincidentally, the majority leader is GOP.
So the GOP, at the last minute the day of the shutdown, amended the House rules to say that only they (GOP) would be able to request re-opening the government.
Please note, I am not either Dem or Rep. They are both snakes, IMO. I'm just illustrating some of the bullshit that's going on, as I found it.