Fear mongering is the use of fear

Fear

Fear is a distressing negative sensation induced by a perceived threat. It is a basic survival mechanism occurring in response to a specific stimulus, such as pain or the threat of danger...

 to influence the opinions and actions of others towards some specific end. The feared object or subject is sometimes exaggerated, and the pattern of fear mongering is usually one of repetition, in order to continuously reinforce the intended effects of this tactic, sometimes in the form of a vicious circle

Virtuous circle and vicious circle

A virtuous circle and a vicious circle are economic terms. They refer to a complex of events that reinforces itself through a feedback loop. A virtuous circle has favorable results, while a vicious circle has detrimental results...

.
Probably the best-known example in American politics is the Daisy

Daisy (television commercial)

"Daisy," sometimes known as "Daisy Girl" or "Peace, Little Girl," was a controversial political advertisement aired on television during the 1964 United States presidential election by incumbent president Lyndon B. Johnson's campaign...

television commercial, a famous campaign television advertisement beginning with a little girl standing in a meadow with chirping birds, picking the petals of a daisy while counting each petal slowly.