Why do the characters in Fahrenheit 451 believe that it will be a quick war?
The characters have all been programmed by the government. They listen to the government propaganda on TV, live the type of life the government feels will make them happy, and don't read books because they have allowed them to die out and the government doesn't want them coming up with any new ideas. As Beatty tells Montag,
"If you don't want a man unhappy politically, don't give him two sides of a question to worry him; give him one. Better yet, give him none. Let him forget there is such a thing as war." (pg 61)
The government totally controls the actions and thoughts of all the people. So, when Montag asks the women who had come to visit Mildred when they thought the war would start, Mrs. Phelps tells him,
"...the Army called Pete yesterday. He'll be back next week. The Army said so. Quick war. Forty-eight hours, they said, and everyone home. That's what the Army said. Quick war. Pete was called yesterday and they said he'd be back next week. Quick..." (pg 94)
Therefore if the Army, the representative of the government, said it, it must be so. The women are still nervous about it, but Millie supports her friend and says,
"....I've never known any dead man killed in a war. Killed jumping off buildings, yes, like Gloria's husband last week, but from wars? No." (pg 94)
And, as we learn later in the novel, it was a quick war.
"And the war began and ended in that instant.
Later the men around Montag could not say if they had really seen anything. Perhaps the merest flourish of light and motion in the sky. Perhaps the bombs were there, and the jets, ten miles, five miles, one mile up, for the merest instant, like grain thrown over the heavens by a great sowing hand, and the bombs drifting with dreadful swiftness, yet sudden slowness, down upon the morning city they had left behind. The bombardment was to all intents and purposes finished once the jets had sighted their target, alerted their bombardier at five thousand miles an hour; as quick as the whisper of the scythe the war was finished." (pg 158)