kaled - 2:00 am on Oct 23, 2010 (gmt 0)
I live in the UK, however I would expect the legal position to be more or less the same.
If you ordered the goods and the merchant arranged delivery then, from your point of view, the merchant is liable. If you arranged delivery yourself (as you might when buying a large item on ebay) then the merchant would not be liable.
Essentially, if the merchant is using a cheap service then the risk is theirs not yours. I recommend you contact your credit card company and simply state the the goods were not delivered. For an item with a value of $50, I would expect the amount to be credited almost immediately unless you have a history of similar problems.
Since you had to ask, I assume that this was not made clear at the time of purchase - in this case, the merchant doesn't have a leg to stand on. Their arbitrary cost-cutting policy does not make you liable for their failure to deliver.
Upon followup, the merchant told me they never require signatures for orders under $200 and wished me good luck in resolving the matter with FedEx.