Right now, we have the following players under contract:
Tatum
Brown
Brogdon
Smart
White
Williams III
Horford
Gallinari
Pritchard
Muscula
Kornet
Champagnie
Hauser
Those salaries, plus the dead cap hit of Demetrius Jackson, total $166,144,883. That's only $4,144,883 above the tax.
If we waive Kornet and Champagnie, that saves roughly $4 million (I'm not sure how much of Kornet's guaranteed amount is).
So, with the following roster, we'd be at right about the tax line:
Tatum
Brown
Brogdon
Smart
White
Williams III
Horford
Gallinari
Pritchard
Muscula
Kornet
Champagnie
Hauser
We'd be approximately $16.5 million below the "second apron", with 11 players under contract. We'd need to fill out at least three spots. And, if we trade Pritchard, we'd save another $4 million, and would have $20.5 million below the second apron to fill out four spots.
(Note: this is largely theoretical, because most, if not all, of the penalties regarding the second apron don't come into affect yet.)
Now, all that said, what we do with Grant Williams will decide whether we're comfortably below the second apron, or if we're close to it. If Grant plays for his $8.5 qualifying offer, we're golden. If he receives closer to his cap hold -- $12.9 million -- it's a finer shave.
Personally, I think the team might be better off trading Grant if he won't play for the QO (which he likely wouldn't). We'd then have plenty of room to use the Taxpayer MLE to add somebody to the rotation.