First Daughter (2004)
There is a poster for the older movie visible.
Ca. 45 minutes into the film, the older movie's title is visible on a theater's billboard.
Ca. 24 min. into the film, the First Daughter is watching Leno talking about her on TV. This is a specially filmed sequence. There is another such scene at minute 87.
Ca. 28 minutes into the film, Mia calls the Secret Service agents guarding Samamtha "fake Men in Black boys". She calls them "Men in Black"-action figures at minute 50.
Ca. 14 min. into the film there are several scenes with people walking incredibly fast through the corridors of the White House while talking incredibly fast, just like they do on the older series.
DVD case is shown.
DVD can be seen in the rental store
Mentioned by Tosh
film is playing at theater that Samantha and James sneak into