"Recent mass shootings have had little impact on the public's attitudes toward gun control. That was the case after the Colorado theater shootings; similarly, views of gun control changed little after the Jan. 2011 shooting in Tucson Arizona, which killed six people and seriously wounded former Rep. Gabrielle Giffords.
The murders of 20 small children and six adults at an elementary school could be just so shocking, of course, that it will move opinion.
The one relatively recent point in time where polls done by both Pew and Gallup show a significant upward movement in favor of making gun laws "more strict" or of making gun "control" more important than protecting "the rights of Americans to own guns" was after the April 1999 attack by two students at Colorado's Columbine High School. They killed 12 students and one teacher before taking their own lives. In both organizations' polls, public opinion in favor of "gun control" hit 66 percent.
Since then, both polling organizations show support more or less steadily declining into the low 40s.
Opinion also might be moved by very public calls by some prominent leaders (such as New York City Mayor Michael Bloomberg) for stricter gun laws.
How public opinion has changed in recent decades.