Hi - I have tried this versus a multinational company and it has worked ! I got all my money owed at the time. As a small business, I was the primary author of the contract. It was a case of the client at the local level not being broke but just not caring. The clients goals are always met, so there is no reason to fire my firm. Now, I am always paid on time. :-) Well what I did was classify my inaction as being due to lack of payment not deliberate - I stated that I did not have the resources to continue working on their project without pay, which has some truth to it. Viola, a perfectly viable excuse brought up at a perfectly bad time, that's all.
You do have a point, review your contract before you try this.