Well, he is doing the people's will as expressed in a referendum, whereas they are Remainers pretending to be protectors of the constitution, but actually defying the will of the people and the UK law which provides a withdrawal timetable and for which parliament voted.
My view is that they have brought this on themselves. They have played games to prevent Brexit or anything resembling it. They have conspired with the EU to deliver an unsignable deal through Mrs May, thereby producing the delays they desire. So the PM has no choice but to run down the clock.
The queen and/or the courts will decide whether his actions are constitutional, of course. "Outrage" isn't a legal position. But I certainly feel their behavior to frustrate a referendum has been outrageous. The default position is that we leave - the PM is confirming the timetable. The coup position is to prevent the UK's departure from the EU and to deny the referendum's result.