In fact, the console will see hard drives up to 2TB, and support for up to two external drives at once. Per Major Nelson:
The next update for Xbox 360 Preview Program members will allow the use of 2TB hard drives to store Xbox 360 data. If you are not part of the Preview program you will get this functionality later this year. In addition we will also no longer reserve space in advance on your hard drive. If you are using 16GB of hard drive space for games – we will only take 16GB of space. And just like today – you will be able to use two external drives at a time.
The update is coming first for Xbox 360 Preview Program members, and will roll out to the wider Xbox 360 user community later in the year. Then you'll have all the space you need to store your Goat Simulator games.
Source: Major Nelson