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<b>をめぐって</b>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<b>をめぐり</b>色々な対立する意見がありあます。　→　There are many opposing surrounding/concerning the President's economic policies.
* 資源の利用<b>をめぐる</b>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.