I found the info for where to write and what needs to be included on the letter to the President here. And lo and behold Emma received a letter addressed to her from the White House! The only place her name appears is on the envelope so be careful opening it if you do decide to write the President :o)
Here's a picture of the announcement we sent with a picture of her on election day:
Regardless of your political leanings I think it is a fun little memento to have. I've heard other places like Disneyland also do something similar.
I also sent for a birthday greeting for my Grandma Dorothy who will be turning 95 this year! But don't tell her it's a secret :o)