The Hojo men were faced with a particular choice, one where both solutions were not truly good ones. They were forced to choose between two poisons of varying toxicity. With their men awoken from their slumber and in fear for their lives, they were forced to consider moving their entire camp in the darkness.
But that would take a few hours at the very least. If they chose to do that, then their sleep would definitely be compromised. With those faces grinning at them from atop the castle wall, the generals were hesitant to run away so quickly with their tails between their legs.
They made a decision, and they decided it was a bluff.
"They'll only have one ball like that," one general proposed, "it'd take weeks to get a respectable amount. If they had any sure amount of them, they'd have turned all their cannons on us already and shot us down with what they could. I say we sleep through this night, and move our camp come morning."