Republicans think you are stupid. If a terrorist group takes a hostage, rest assured that 99% of people will blame the terrorist group if the hostage is hurt or killed, and not the hostage's allies who were not in a position to give in to the outrageous demands of terrorists. But Republicans have convinced themselves that they can get the public to blame the Democrats for the government shutdown caused by Republicans taking the government hostage.
Republicans are trying to convince everyone that they hate this shutdown and wish it weren't happening, which of course flies directly in the face of their repeated gleeful celebrations of the shutdown that indicate that they fucking love this because anything that pisses off the liberals and hurts poor people is a win in their book. They're shedding crocodile tears over the closing of the WWII monument that they are responsible for closing. Ted Cruz is literally threatening terrorism, saying that the shutdown leaves us vulnerable. In other words, he is straight up saying that the minority party should get what they want or people will get killed. That's some ugly, dark, evil shit.
As with many things, the diehards are convincing themselves they believe the lie that this is the Democrats' fault, but I doubt anyone else is. Republicans have done a terrible job of trying to convince us that this is anything but punishment for electing the "wrong" party into the White House. It's amazingly childish, like hitting your brother and trying to convince your mom he did it to himself. Except these assholes are presumably adults.
The fact of the matter is Boehner probably could stop the shutdown tomorrow morning if he wants. He has the votes. They won't because they don't want to reopen the government. They want to punish us for daring to defy them and voting how we want instead of how they told us to vote. It's unsurprising to me that the GOP uses some of the common tactics of domestic abusers, namely gaslighting the voters (trying to make them believe what they know---that the GOP is behind this---isn't true) and claiming that it's the victim's fault that they "had" to hurt them. They are, after all, the party that backs an increasingly rigid and abusive sexist ideology that fits quite neatly with those rhetorical devices. But we have no need to believe them.