It has happened before and can happen again. If Congress does not pass a spending bill today, the federal government has no lawful authority to spend money tomorrow.
Remember, though, this whole "crisis" exists because one party had control over the entire appropriation process--and failed to get the job done last year. The other party now has control of the house in which spending legislation originates and has done its job, passing a spending authorization. The hang-up is the house that is still controlled by the party that failed in its job, the leadership of which refuses to even consider the spending bill that has already been sent to it for action.
On edit: This is not OC-related. The thread belongs in the Social Lounge.