In additions to what @sawa said, I think it's easy to keep straight if you remember the verb めぐる
has the meanings of "going around" or "surrounding". Thus, ~をめぐって/~をめぐり/~をめぐる
usually has at least a slight negative meaning (as @sawa stated) usually about some debate, controversy, etc.
Here are a couple examples. (I'm going to expand on one of @sawa's because I feel it's a little too vague to be helpful to you -- no offense to @sawa).
- 駅の改築をめぐって近くの店主がたくさん集まってデモる。 → Many of the nearby store owners will gather and protest the reconstruction of the station (protest surrounding the reconstruction of the station
- 大統領の経済政策をめぐり色々な対立する意見がありあますます。 → There are many opposing opinions surrounding/concerning the President's economic policies.
- 資源の利用をめぐる争いがようやく解決に向かった。 → The dispute about/surrounding the resource usage is finally headed toward a solution.
As far as the sentence you provided, the controversy is that there are obviously some people who hold the opinion that a political parties only exist to get the upper hand in an election (by doing the things listed), instead of focusing on meeting the peoples' needs.