snowball into (something)
To develop quickly and progressively into something bigger, more complex, more difficult, more dangerous, etc. This whole situation could snowball into a national scandal if the press gets wind of it. It started out as an idea for a short story, but I just kept adding details and characters and plot twists to it until it snowballed into a full-blown novel.
snowball into something
Fig. [for something] to become larger or more serious by growing like a snowball being rolled. This whole problem is snowballing into a crisis very rapidly. The argument soon snowballed into a full-blown riot.