How much would it cost to fix a riding lawn mower for the governor?

The cost should not be more than twenty dollars from just about any Sears store. You might try one of the guys who repair small engines in your area, he might have one on hand for some less than Sears would charge.
Look first at the vein return spring to see if it has not come off. Usually this is exactly what the problem is and takes only a few minuets to remedy with no money spent on pieces not needed. If the spring has sprung most hardware stores have springs that will do the same job for some cents rather than some dollars. Will it be made from the same kind of steel? Yes it will. The only difference is that you did not buy it from the Sears parts guys.