It's unclear if this was intentional or not, but at one point during the President's birthday party near the end of the show, a short black woman walks up to her and wishes her a happy birthday. This looks startlingly like Michaëlle Jean, Canada's current Governor General.
At one point, Jim, the President's Chief of Staff see's the President's aide, Vince, holding a bow and arrow. Jim says, "I'm betting this president can handle a bow and arrow." This comment is an inside joke as Geena Davis, who plays the President almost made the 2000 US Olympic Archery team in 1999.
The episode title, "Happy Birthday, Madam President," is an allusion to Marilyn Monroe's tribute to President John F. Kennedy at his May, 1962 birthday celebration in Madison Square Garden.
Wearing a racy dress, Monroe sang the traditional birthday song, "Happy Birthday To You," in a sensuous tone and substituted "Mister President" where the birthday person's name is usually inserted. One of the sex symbol's last public appearances before dying from a drug overdose, the incident became notorious and fueled speculation that the two were having an affair.
Her performance of "Happy Birthday, Mr. President" was taped and has repeatedly been broadcast, referred to, imitated, and parodied.