The latest as of today is to reference what happened last year. While the state couldn't agree on a budget school's allowed students to enroll, then worked out financial aid issues after the fact. IIRC it was about the same week as school beginning for some.
School's know when the funds are disbursed, so they are patient with you and should let you stay enrolled. Typically the only consequence for non-payment is a hold on your account, so you should be able to complete a semester if it went that long. The only problem you should have is if you need the cash difference for books or off-campus housing and expenses.
There will most likely be cuts in grants and loans, but without knowing yet what the cuts will be or your situation we can't know yet how they will affect you. Most likely they won't for this year, but you may not qualify for the next.
More likely ways that it will affect you this year are in class cancellations and impacts on registration. It will be another inconvenient year for students.