Ok, now seriously. NEVER EVER EVER!! send out a mass email with that many people in the To address. If ever you need need to send out emails to many people, put them all in the BCC field, and yourself or a no-reply address or something like that in the To field. If you don't, someone is 100% certain to forward the email, it gets forwarded a few times more and in the end some spammer gets it and has an extra 2000 email addresses to spam to.
Now ontopic. Whenever you put all 2000 addresses in the BCC field instead of the To field, you're very likely going to get the same problem. Now why 2GB shouldn't be enough for 2000 addresses (that's just over 2MB per address!) is something I can't answer you. Do you get the same problem if you use only 500 users? Are you adding huge attachments?