The Google App Engine is perfect for this. You also do not need to move your entire application, just create a web service into which you upload your email and protect it so that no one else can transfer it. They do not provide smtp or the mail interface, but you get the opportunity to run it on the scalable Google infrastructure and a generous free discount so you can test it fairly reliably for free.
You will need to create a client that connects to the web service and starts emails in batches to bypass their 30 second page life cycle limit, but if you created another web service to download the actual email template, then all that you need to send when the email schedule is a bunch of addresses. It is better to repeat the survey of your web service with a small amount of data, and this is quite acceptable behavior regarding google.
They allow you to send 2,000 letters per day @ 8 letters per minute with a daily income of 60 MB - before you receive the bill.
If you activate billing, these limits change to 7.4 million recipients per day with a maximum limit of 29 GB for the total body size and 100 GB of investments.
http://code.google.com/appengine/docs/quotas.html#Mail