I found a couple of data sources that might be of interest for NFL data. This first one is this one:
Which gives you the scores per game per quarter
and this site gives live data also and you can choose by date and has many more details
Then there is also this one here which is in XML
Now, I have no idea how the data looks like while there are active games but we should be able to see that during next weeks games.
IF the NFL updates these data feeds quickly, an App could be made that queries the data "regularly", filters for your team and performs an action when the score changes.
Food for thought and food for a hungry NFL fan developer...