1) Politicians don't care about constituent's current opinions, but about their future response to actions the politican might undertake. For example, recent articles indicate widespread support in the U.S. for gun control, but a politician might anticipate: If I support a gun control measure then the NRA will run ads in my district; that will change many opinions [1], spread other negative stories about me, and galvanize my opponents both in public discussion and when getting voters to the polls.
2) The large differences between different subgroups explain the difference: All constituents, all voters, primary voters, and the few who vote in state legislative elections. (I challenge HN readers to name your state representatives without looking them up.)
If these issues are covered in the paper, I apologize; I read what I could now and searched the paper for related terms, but won't have time to finish reading until much later.
----
[1] I don't know that ads have this effect. My impression is that most people's opinions are weakly held and that they follow the herd on most issues (whichever herd they feel they belong to).