The 112th Congress was a very productive session. Among its accomplishments were the Budget Control Act (which created the mess that is sequestration), the extension of warrantless wiretapping with no accountability, and an attempt to wreck the Iranian economy. Good job, guys!
I kid, I kid...
Besides its historic lack of productivity, the 112th Congress is also one of the most polarized. Although this has been studied in various ways, it is illuminating to look at the historical change in ideological stance of the majority maker in the House, the person one would have to win over in order to reach the 218 threshold. The DW Nominate scoring system, which evaluates all Senators and Representatives on a scale from -1.00 (most liberal) to 1.00 (most conservative) based on Roll Call votes, offers a useful framework for this. With the DW Nominate Score, you can track how far from the center (either left or right) that the majority maker was in each congress.
Because this rating system includes all members, each rank ordering will contain duplicates for a district if a special election occurred during that session. Nevertheless, we can get a rough idea of the ideological rating of the majority maker in each session.
The majority maker of the 112th Congress, according to DW Nominate, would be either Jo Ann Emerson (R-MO-08) or Frank Wolf (R-VA-10). Emerson received a rating of 0.268 and Wolf 0.270.
Taking a span of the postwar era, majority makers whose rating were over 0.200 from the center point were quite rare, characteristic of only wave elections such as 1964 (LBJ's landslide victory), 1974 (post-Watergate), 2008 (Obama's victory amidst the economic crisis), and 2010. However, in 1964, 1974, and 2008, the majority maker in the incoming House was always close to 0.200 from the center (even though slightly passing it). The current Congress, however, pushes much further past that traditional outer bound, and despite the Democrats' gain in seats in the new Congress, the ideological rating of the majority maker is unlikely to shift much.