Your mistake is using the datetime module instead of the date module. You meant to do this:
from datetime import date
date = models.DateField(_("Date"), default=date.today)
If you only want to capture the current date the proper way to handle this is to use the auto_now_add parameter:
date = models.DateField(_("Date"), auto_now_add=True)
However, the modelfield docs clearly state that auto_now_add and auto_now will always use the current date and are not a default value that you can override.
This is why you should always import the base ABC0 module: import datetime, rather than the datetime class within that module: from datetime import datetime.
The other mistake you have made is to actually call the function in the default, with the (). This means that all models will get the date at the time the class is first defined - so if your server stays up for days or weeks without restarting Apache, all elements will get same the initial date.
So the field should be:
import datetime
date = models.DateField(_("Date"), default=datetime.date.today)
Automatically set the field to now when the object is first created. Useful for creation of timestamps. Note that the current date is always used; it’s not just a default value that you can override. So even if you set a value for this field when creating the object, it will be ignored. Source: Django
doc
I think a better way to solve this would be to use the datetime callable:
from datetime import datetime
date = models.DateField(default=datetime.now)
Note that no parenthesis were used. If you used parenthesis you would invoke the now() function just once (when the model is created). Instead, you pass the callable as an argument, thus being invoked everytime an instance of the model is created.
HINT: It seems you set a fixed date / time / datetime value as default for this field. This may not be what you want. If you want to have the current date as default, use django.utils.timezone.now