The administration probably doesn't have the legal authority to do this. Under federal law, a machine gun is defined as "any weapon which shoots, is designed to shoot, or can be readily restored to shoot, automatically more than one shot, without manual reloading, by a single function of the trigger." But a gun equipped with a bump stock is still able only to fire just one round per trigger pull. "Instead of squeezing the trigger, the shooter holds his trigger finger steady while pushing the barrel forward with his other hand, thereby firing a round," Reason's Jacob Sullum explains. "The recoil repositions the trigger, and continuing to exert forward pressure on the barrel makes the rifle fire repeatedly."
As Reason's Christian Britschgi explained in March, this is probably why the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) has said multiple times that federal restrictions on machine guns do not cover bump stocks. The Obama administration affirmed the legality of bump stocks on three different occasions: once in 2010, again in 2012, and once more in 2013.
As Sen. Diane Feinstein (D–Calif.) said in a February statement: The ATF "currently lacks authority under the law to ban bump stocks."
In addition to being legally questionable, a bump stock ban probably wouldn't do very much. No mass shooters before or after Las Vegas have used bump stocks to carry out their massacres. Even in Las Vegas, the death toll wasn't necessarily higher because the shooter used one.