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Timothy
First, get another quote on the timing belt. It's a tough job, but the engine does not have to be pulled. Also, keep in mind that usually the mechanic will suggest replacing the belt tensioner, water pump, other belts, etc. at the same time.
As for covering the cost with an extended warranty. It's unlikely that it would be covered. The belt replacement is a maintenance procedure.
From a prior forum answer:
Is an extended warranty advisable?
This is a tough subject, and it is hard to give a good
answer. If you get one (normally $1,500 or so) and nothing goes wrong, you may
get mad for spending the money. But if you experience serious engine or
transmission problems you may regret not having made the purchase. The expected
reliability of your car is a major factor. Check the CR
comparative reliability Ratings. The less reliable a car is, the
more likely you are to benefit from an extended warranty.
If you decide to get one, read the fine print on the
warranty papers carefully. A common problem with extended warranties is that
they are not as broad as the original manufacturer's warranty. For example,
brakes may not be covered, so you would have to pay for that in full. Also,
many extended programs have a $200 - $300 deductible. Normally a good portion
of common repairs will cost less than the deductible. So you may end up paying
$200 - $300 repeatedly before the warranty takes over. Again, read the coverage
and fine print closely, and think of an extended warranty as catastrophe
insurance.