Principal photography is usually the most expensive phase of film production, generally due to actor, director, and set crew salaries, the costs of certain shots, including any props or on-set special effects. Its start generally marks a point of no return for the financiers, because until it is complete there is unlikely to be enough material filmed to release a final product needed to recoup costs. While it is common for a film to lose its greenlight status during pre-production (for example, because an important cast member drops out), it is extremely uncommon for finance to be withdrawn once principal photography has commenced, and it is usually regarded as a catastrophe.
Please NOTE what Hoffman said in the PR. "principal photography........ will start on Monday, January 16th in New Orleans."
THAT means the plug could be pulled anytime before that. (see definition above)