It's difficult enough to come up with a great costume idea for just one person, but it becomes even harder when you're looking for a two-person costume idea. Playing up on the idea that opposites attract is an interesting way to approach the challenge. Look for costume ideas for people that you wouldn't normally see together and you'll amuse everyone at the next party.
Sports fans are notoriously loyal, so you can create an opposites attract costume by dressing as fans of rival teams. For example, you could dress as Yankees and Red Sox fans. All you really need for the costume is a few pieces of clothing that reflect the sport, such as T-shirts or jerseys, but you can add even more details with hats, facial paint and large signs.
Using the "good" of religious icons makes for a nice contrast with more seedy elements. You could dress as an angel and a devil, which is a classic costume for couples. Another idea is to have one person dress as a priest or a nun, while the other dresses as a stripper.
Teen cliques can also make for an opposites attract costume, as you don't often see different groups intermingling. You can dress as a nerd, a jock, a goth, a prep or a punk and have the other person dress as something different. Try to mix things up. For example, in movies, it's not uncommon for the pretty, popular cheerleader to eventually fall in love with a nerd, but it's not as likely to see the star football player falling for the punk rock girl.
It's in science that we get the idea of opposites attracting, so it makes sense to draw your costume ideas from science. You can dress as electrons and protons or a positive and negative magnet.
It seems that democrats and republicans are about as opposite as you can get. You can purchase rubber face masks that allow you to dress as a specific politician. Alternatively, you can simply dress as protesters on either side of the fence--a few funny protest signs will surely show the difference.