The shooting in Dallas on July 7, 2016, does not track "the narrative" in several ways, one of which is that the shooter did not use an AR-15 or any other so-called "assault rifle." Rather, he used an SKS--a simple antique (late WWII - era) semi-automatic rifle fed from a fixed box magazine. Not being able to resort to the tired "weapons of war" phrase, President Obama had to change his message: "'When people are armed with powerful weapons, unfortunately it makes attacks like these more deadly and tragic,' Obama said. 'In the days ahead we're going to have to consider those realities.'"
What was powerful about the weapon? Was it because of the power of cartridge? If so, it is important to note that the 7.62x39 mm is an intermediate power cartridge, far less powerful than most other calibers used for hunting.
Was it because it was a semi-automatic allowing rapid follow up shots? If so, it is important to note that many popular rifles used for recreation and hunting are semi-automatic. Would it have made any difference if the shooter had been using a bolt action rifle? (If you believe so, you should watch how rapidly a practiced rifleman can cycle a bolt action rifle (starting about 2 minute mark)). Or a lever action?
Was it because the SKS can be reloaded using a stripper clip (aka charger)? Many other antique rifles can be loaded using clips or chargers, and many modern hunting rifles (semi-auto. bolt action, and pump action) use detachable box magazines that are even easier to use.
In short, any hunting rifle would be a "powerful weapon" if used as a weapon.
Update (July 10, 2016):Originally, the Daily Mail had reported that the rifle was an SKS. Now the Daily Mail is being reported that the shooter used an AR-15. However, it appears that weapon used was a scoped AK-74 variant.