"The Brink" is most certainly a political satire and not a comedy. The exaggeration and the ridicule is obvious from the start. But sadly not far from the truth...
It's about a fictional U.S. government which must deal with a foreign crisis. Its first season focuses on a crisis in Pakistan. The show was conceived that each season will follow a different crisis somewhere in the world with the same characters. (IF it gets a 2nd season that is!).
There are a few main characters. An alcoholic Secretary of State played by Tim Robbins, a lowly Foreign Service officer in Islamabad played by Jack Black and lots of other known comedic actors in various roles.
It is mildly funny because of these talents but if you go for the satire you might need a sharper bite. It seems like the creators went for some kind of Dr Strangelove type of thing, but fails short to deliver any real political messages.
Overall: Basically I would say "Meh!" but the cast is good so I will keep watching for now.
UPDATE (after watching the whole season): It gets better and 9th and 10th (season finale) episodes are GREAT! Highly Recommended!!