Scour the vaguely legal sites
We can't condone piracy, but when you're desperate, you're desperate. Sites like FirstRow and ATDHE have each proven fruitful in the past, so poke around and you might very well find a semi-decent stream. Just be prepared for a deluge of janky pop-ups and some serious sub-HD quality.
Reddit's full of helpful advice beyond how to urinate like a pro or score free in-flight Wi-Fi. In fact there are entire sub-Reddits that dedicate themselves to maintaining a real-time list of quality (and free) NFL streams. Do yourself a favor and bookmark this one.