I have the same question (I'm brand new to CC). I want to create an app that uses the CC API to send emails to our customers. This app would run every day and will need to add new email addresses, however the email should only be sent to the new email addresses (i.e., not to recipients that have already received the email).
Currently we do not offer any API method for pushing Campaign Content or for scheduling and resending email campaigns. We are constantly working on expanding the API and this is one of our feature requests we are looking back. We update the developer website when we offer any new functionality to the API.
Regarding the resending option you're describing, we do offer the ability to resend a campaign to new contacts since the last send. This is available for 85 days after the original send of the email campaign. Currently this feature is only available through the Constant Contact UI and can not be automated currently.