I feel extreme violence does speed up government response, as it brings home to the general person just what is going on in that location. In turn, this makes the government want to do something to show they are reacting, and not standing for it. I think is more noticeable when an election is approaching.
Yes, extreme violence speeds up government response on issues which have been prevalent for some time because extreme violence catches the media's attention and the people then require action from the government. It is my opinion, the issues with ISIS in Syria have been a problem for longer than the air strikes have been happening, but because of the beheading of Americans and allies the government began to take action.
Beheadings and bombings call attention to situations that may have fallen onto the back burner. If nothing is happening then many times officials feel like they can wait and see what happens before they react. Once something tragic happens then they are compelled to act to ease the minds of the public.
Yes I do agree that extreme violent acts such as be headings and bombings will speed up a governments response on issues. When things like that start to happen than the general public gets involved and that will bring it more to the governments attention maybe even more than the incidents themselves.
Government responds as per their national and global strategy . For example Bush responded in one way , when confronted with 9 -11 , we are not sure if Obama would have responded in a similar fashion . I guess Bush wanted to go war with Iraq and just used 9-11 as an excuse. Sometimes Government may use events to tighten their control and take way people's rights. There is also question of false flag events , when Government triggers an event to do a certain thing . This has happened in many cases in USA history . Eg starting the war with Vietnam , when Vietnam was supposed to have a USA ship , but actually there was no such event .