The Republicans in the House keep whining that the government shutdown is not their fault because they tried to "compromise" with the Democrats and were rejected. They are either lying, or they are too stupid to understand the concept of compromise. I'm betting on the former.
It is not a compromise to demand something you know your opponent cannot give you, even if you reduce that demand to something else you know cannot be accepted (or even discussed). The Republicans knew the Democrats (and the president) could not and would not repeal, defund, or delay the Affordable Care Act. That's why they demanded it -- because they wanted the shutdown to make their teabagger base happy, and the best way to do that was to harm the government (which the ultra-right-wingers hate).
Some may think the cartoon above is a bit over-the-top. I don't. By demanding that Obamacare be repealed, defunded, or delayed, the Republicans were demanding that millions of Americans should continue to be denied health insurance, which would deny them access to health care (especially preventive care) and put their lives in danger. And they did that purely for political purposes.
The Republicans haven't tried to compromise on anything since President Obama was elected. And those who claim that they have are liars. There's no nice way to put it.