I am using the basic-auth twitter API (no longer available) to integrate twitter with my blog\'s commenting system. The problem with this and many other web APIs out there
Your method has a flaw - if someone were to intercept the transmission of the key to the user and the user's encrypted reply they could decrypt the reply and obtain the username/password of the user.
However, there is a way to securely send information over an unsecure medium so long as the information is not capable of being modified in transit known as the Diffie-Hellman algorithm. Basically two parties are able to compute the shared key used to encrypt the data based on their conversations - yet an observer does not have enough information to deduce the key.
Setting up the conversation between the client and the server can be tricky though, and much more time consuming than simply applying SSL to your site. You don't even have to pay for it - you can generate a self-signed certificate that provides the necessary encryption. This won't protect against man-in-the-middle attacks, but neither will the Diffie-Hellman algorithm.