Python API Query + Email Notification
Looks good at a first glance.  For reusability the code should be
divided into functions instead of just being a single script file.


I'd load the multiple environment keys in a loop and into a separate
dictionary instead of globals.  That's nicer to refactor later and
it's easy to pass around, or even update from command line arguments
as well (e.g. using argparse).  You can also look at
dotmap or something similar to
get a bit nicer syntax.  E.g.:

options = {}
for name in ["MIN_DAYS",
            "TRELLO_KEY",
            "TRELLO_TOKEN",
            "TRELLO_BOARD",
            "MANDRILL_KEY",
            "MSG_FROM_EMAIL",
            "MSG_FROM_NAME",
            "MSG_SUBJECT",
            "MEMBER_EMAILS"]:
    options[name] = os.environ.get(name)

The loop at the end can be exited early with
if ... not in ...: continue to remove one level of indentation.
The print should be using function call syntax for forwards
compatibility with Python 3 and similarly the except handler should
also use the except ... as e: syntax instead.  I.e.:

...
        print(result)
    except mandrill.Error as e:
...

The iteration over members can use iteritems to get both name and
cards in the same step.
For the date comparison I'd recommend using a dedicated library, that
way both the code will be easier to read and one less wheel is
reinvented.  E.g. I had good experiences with
arrow.
For the HTTP requests you can also look at
requests for a nicer
interface.