Was looking at 12 years a Slave's box office numbers and found something interesting. It's foreign numbers were pretty damn big.
12 Years a Slave (2013) - Box Office Mojo
Domestic: $56,671,993 30.2%
+
Foreign: $131,061,209 69.8%
=
Worldwide: $187,733,202
The strong majority of 12 Years a Slave's numbers came from overseas, not the U.S.. This is important as 12 years was distributed by Fox Searchlight, just like Birth of a Nation.
Also keep in mind that 12 years a Slave was financed by film studios unlike BOAN and was more expensive to make than BOAN, at the cost of $22 million.
In short, whether or not Birth of a Nation is a financial success or not may come down to how it does outside of the U.S.. If Fox is on their jobs, they might pull it off.
EDIT: Did additional research. Lionsgate distributed 12 years a Slave overseas, while Fox Searchlight did the domestic distribution. I wonder if this same approach will be used for BOAN.