rush on

rush on something

 and run on something
a large demand for something. There was a rush on bottled water during the drought. During the hot summer, there was a run on air conditioners.
See also: on, rush
References in classic literature ?
Old Brooke takes half a dozen quick steps, and away goes the ball spinning towards the School goal, seventy yards before it touches ground, and at no point above twelve or fifteen feet high, a model kick-off; and the School-house cheer and rush on.
And away comes the ball, kicked high in the air, to give the School time to rush on and catch it as it falls.