Putting aside the causation behind mass shootings for a moment (again mental illness and guns aren't new) and squarely looking at gun control - we see that the appetite for greater restrictions were there well before Parkland. Gallup has surveyed on this question with its regular polling since 1991. It's useful as a baseline for the average adult's wishes before the Parkland shooting.
In January, an average of 60% of adults wanted stricter gun control federally
What's more is that the trend has been rapidly moving in favor of more gun control. In 2014, 47% wanted more gun control. In 2015 & 2016 it was up to 55% and as mentioned we were up to 60% prior to Parkland. It's clear that the increase in mass shootings in the US - regardless of circumstances - has led to an increase in the collective's desire for gun control. The first related post-Parkland poll from ABC/Washington Post indicated that 58% think stricter gun control might have prevented the shooting at Marjory Stoneman Douglas. With thoughts like that it's clear that the momentum will continue to build for additional gun control measures to take place. What's the most desired action in the wake of the Parkland shooting?
77% additional/more effective mental health evaluation
58% further restriction on ownership
42% allowing teachers to carry on campus
The concern for many lawful gun owners is what the goal is of gun control advocates. According to Gallup's most recent work from January, 28% wanted to ban private ownership of guns (allowing only law enforcement access). That gives you an idea about how many are motivated above and behind what they're indicating publicly. With public opinion as strong as it currently is and elected officials from Tallahassee to Washington D.C. considering action - it's likely change is coming. The question is simply what it looks like.