Was the warranty on the car for 60,000 miles or the engine for 60,000 miles? Was it the timing belt or the accessory belt? If it was either belt that broke, it was well past time to have been replaced, then you are sol. If the the warranty on the car expired at 60,000 miles, and the belt was replaced prior to that point on schedule, but you missed this one by 2,000 miles, you are sol.

Based on what you said: The only way for the dealer or manufacturer to warranty this is: And I am making an educated guess on this: They will say that engine failure was not the result of manufacturer defect, but defect of the belt or the lack of proper timing for the replacement of the belt, which caused the the belt to fail due to it being in service for a time period beyond for which it is designed. They will tell you to take it up with the belt manufacturer, who in turn may simply give you a new belt.

You may want to talk to an attorney.