Is there such a thing as an open source PHP ecommerce API? That is, just the API (i.e., not a whole CMS etc.). I just want some sort of "library" I can invoke from my own code. All of the open source ecommerce solutions that I've run across (such as http://www.opencart.com/) include a whole UI, etc., which I don't want.
You are most probably looking for the wrong thing. The "CMS", a.k.a. Shopping Cart System, is just a CMS, there is no API and there can't be one, it's just a content management system.
What you're most probably looking for is a payment system API? Like PayPal API, or 2CO API, the payment functions of which you can invoke from your code, like [Pay $20!], which transfers over to a PayPal Pay page, and they take the payment processing on from there.
Otherwise, you may also be interested in Google Checkout https://checkout.google.com/sell/ which has its own API, more information here: http://code.google.com/apis/checkout/
...or the eBay API http://developer.ebay.com/common/api/ if you want to connect your code to and use eBay for all processing.
If this does not answer your question, please provide more information as to the requirements you are actually expecting from this "API".