Let's attack aggressively
You're right of course that it isn't simple at all. You're also correct to point out that both the Democrat and Republican parties are coalitions of smaller groups. The Republican party is a good example, where you have fiscal conservatives, libertarians, social conservatives and religious groups. There's overlap between these, of course (it wouldn't be much of a coalition otherwise), but these groups would be better represented as separate and distinct parties.
Ultimately I believe that having huge overarching coalitions like this is harmful. The reason is that (for example) "Republican" politicians must be seen to represent all of those minor groups. Not every libertarian is a social conservative, but must be seen to be in order to placate those voters. If you want an example, simply look no further than last year's Republican presidential candidate Mitt Romney, a perfect example of a chameleon politician who stands for nothing and anything that will get him that magic 50% of the vote. A two party system actively encourages this kind of self-serving, two-dimensional candidate.
Yes, but isn't that a tautology? In a way, "left wing" and "right wing" are simply artifacts of the two party system itself. All "left wing" really means is "has some slight ideological overlap with other groups that are considered left wing and are therefore Democrat".
Yes, but isn't "interest group" really just a synonym for "political party"? Other countries actually have such parties. Even if parties like these are too small to win enough votes, a multi-party system provides more ability to express real choice, as fringe voters like these can vote for parties who best represent their interests.
Smear campaigns are also an inevitability of a two party system: when there are only two choices, each candidate has only one opponent. Smearing your opponent makes perfect sense when using First Past The Post as your voting system: at minimum it can decrease the votes for your opponent; at best it may drive voters to you instead (as there's nowhere else for them to go).
The thing is, we are a two party system, not because its the law, but because it evolved to be that way. There are actually thousands of parties in the United States, the thing is that they just don't get a much attention as the two more well established parities. In regards to interest groups, it is not a synonym for a political party, because it could be composed of people who have different politics. The goal of an interest group is to focus on a specific cause that they all share. For example, the NRA, AARP, or Mother Against Drunk Driving are interest groups, which could contain democrats, republicans, or independents.