Butt Monkey / Funny Background Event: Before the alien war, Whitmore took a lot of crap from others who either hated his policies or felt that he was too young to run a country. Much of what happens on the new prior to the attack is pretty much everyone badmouthing him.
Chekhov's Skill: See above: Whitmore's tour of duty as a fighter pilot in the Gulf War.
Everyone Calls Him Barkeep: OK, show of hands, who actually remembered that the character's name was not "Mr. President" without having to look it up?
A Father to His Men: Becomes indisputably true during his brilliant Churchillian speech right before the final battle.
Last Stand: Right before the final battle, President Whitmore gives one of the most memorable speeches in movie history, a speech that seems to be deliberately designed to be similar to Churchill's refusal to surrender.
Reasonable Authority Figure: Upon seeing David again for the first time in years, when David punched him in the head, he immediately says he doesn't have time for this. However, he then decides to give him a minute and after hearing about the countdown, Whitmore immediately orders General Grey to begin evacuating the cities.
Badass: He's the only one who survives the Black Knights massacre and even menages to capture an alien, making his attacker crushing in the desert and then knocking him out with a single punch without showing any sign of fear.
Brilliant, but Lazy: He had the talent and knowledge base to becomes a wealthier engineer, but he was perfectly happy where he was.
Character Development: He started out as a Brilliant, but Lazy cable guy, who hated smoking and berated everyone for minor acts of pollution such as littering. After the invasion he starts smoking cigars, making messes and saving the world using a computer virus.
Ivy League For Everyone: Spent eight years at MIT (Massachusetts Institute of Technology), which is the equivalent in status for math & science.
Jewish and Nerdy: His nerdiness ends up serving him well by allowing him to save the world.
Number Two: To President Whitmore. At the beginning of the movie, he requests to stay at the White House alongside the President (it turns out to be lucky. The rest of the JCS were apparently killed by the aliens after they evacuated to NORAD). Throughout the movie, Grey is unfailingly loyal to Whitmore and might be either the new Secretary of Defense or even the new Vice President at the end, given the fact that the former VP is dead and the former Secretary of Defense was unceremoniously fired.
Beware the Silly Ones: When he's not being a Papa Wolf he's a bit of a Cloud Cuckoo Lander, talking about looters and Area 51. However when shit hits the fan he's the first to pull a shotgun out....accidentally at his son, but the thought counts.
Double Tap: Performs this on a wounded alien after he and several Secret Service agents gunned it down.
Reasonable Authority Figure: In spite of being in charge of a highly secret military base, he unlike most fictional characters in such a position is portrayed as a professional soldier who's response to an imminent alien attack is letting all the unauthorized civilians take shelter in the underground laboratories and personally take charge in the evacuation efforts.
Secretary of Defense Albert Nimzicki
Played by: James Rebhorn
Jerkass Has a Point: Sir, if we don't strike soon there may not be much of an America left to defend.
Obstructive Bureaucrat: Does nothing but provide bad advice to the President, and withholds crucial information (regarding the Roswell crash and Area 51) that could have been more useful had it been divulged earlier.
The Scrappy: Both to viewers, and in-universe, to the point where a furious and exasperated President Whitmore finally fires him.
Skewed Priorities / The Sociopath: It's outright stated in the book that he cares more about his political career and legacy than saving the human race from extermination.
Ungrateful Bastard: He's the only one that still acts like an asshole even after many times he's been proven wrong.