When pollsters asked people three decades ago how they felt about the National Rifle Association, 27% said they strongly supported the gun lobby. By last month, that share had grown 38%, an 11-point increase. Meanwhile, the share that didn’t side with the NRA declined.

That is just one measure of the challenge that has forced President Barack Obama to sidestep Congress and put in place new gun regulations through executive action. Mr. Obama knows through hard experience that lawmakers have little appetite for passing tougher...