Let's call it 10 emails a day, at 20kb each. That's 200kb per day. There's 1024kb in a MB, which we'll round to 1000KB.
That means you're hitting a MB per 5 days, resulting in you reaching a 3MB cap in half a month, excluding the very likely issue of attachments raised by Bla1ze above.
Based on these figures, I would imagine that 3MB is not enough, at all.
(Hope my maths is correct, it's late and I've had a few).