A couple of things:
1. The Crownlands are a bit of a muddle. Some of them – the islanders – are sworn to Dragonstone, so there’s 3,000 men right there who can’t be called on. Others, as I’ll discuss in the next Davos chapter, clearly side with Stannis despite not being sworn to Dragonstone. Still others are Targaryen loyalists who don’t give a damn for the Lannisters and Baratheons and who sit out the war. And I think some of them do get drafted to replace some of Tywin’s losses, otherwise there’s no way to explain how Tywin’s army stays at 20,000 throughout the war.
2. Well, Cersei kind of already has. If you apply the 1% rule of premodern societies to the population of King’s Landing, you get 5,000 men that can be raised. And Cersei increases the Goldcloaks to 6,000 men, really scraping the barrel. It’s not clear that the government can support more than that.
But 60,000 is out of the question. The whole Crownlands is around 15,000 men.