At the root of legitimacy is the belief of the people that the government can and will protect their life, liberty, and pursuit of happiness. During the Obama administration it has become obvious that the authorities can't or won't protect us here at home.
Personally, I have great respect for our law enforcement agencies... but they can't be expected to make up for the disaster Bush, Obama, and Hillary created in the Middle East. We decided not to fight our enemies there, so now we're fight them here.
The most disturbing aspect of recent terror attacks is that the authorities were taken by surprise each time despite advance warning. This serial failure undercuts the administration's claim to competence.
This is something the non-expert public understands. Suppose someone came to you claiming he was a brain surgeon. Even if you were not a doctor but had questions only a brain surgeon could answer correctly, you could evaluate the "brain surgeon" by giving him one exam and another to the cleaning person in the hallway. If they scored the same, you would begin to suspect the brain surgeon might be fake.
If the cleaning person continually outscored the "brain surgeon," a rational employer would consider hiring that person as head of surgery, which possibly explains the rise of Donald Trump.
The administration's demand for more gun control crucially rests on the claim of competence.