Filetwt (really going for no vowels) allows you to upload a file no more than 20MB and send it out via a tweet. A simple way to do both public and private tweets with file attachments done for you. You can also create friend lists for easier bulk sharing notifications.
You need to create a Filetwt account as well as enter your Twitter username and password so it can posts your tweets. They do not hook together (they really need oAuth working to make life easy and simplify logging in).
I tried to check the Terms page but it gave an error. I have no idea how long they store your file or make it available. I have no idea if it is private and only you have access to it if someone could figure out the string to see them.