Can I change the tax package? I prepped my taxes but at checkout it's asking me to pay for 2 Self-Employed packages (neither my wife or I are self-employed).

There have been changes made to TurboTax Online. Please see these TurboTax FAQs for more information:

Why did I have to upgrade my TurboTax Online edition?

Who can file for free using TurboTax?

But I don't need 2 packages for a spousal return do I? I can't find a way to delete one of these before checking out and I don't want to pay double the cost for no reason.

At the very least, neither of us are self-employed and so we should at least be able to file both returns with the basic package.

If you prepare your return together with your spouse, then you will both will be using the same version of the program, and you will both be charged the same price. You can only prepare your returns in different products if you prepare your returns separately. 

This TurboTax FAQ lists some possible reasons why TurboTax is telling you that you are self-employed: Why is TurboTax telling me I'm self-employed?