How did the Republicans keep their majority in the House of Representatives?
In the Senate races, where 33 seats out of 100 were at stake, the Democrats not only held their Senate majority but actually picked up a net gain of two seats. If we include two formally Independent Senators who will caucus with the Democrats (democratic socialist Bernie Sanders from Vermont and Angus King from Maine, who took the seat formerly held by the "moderate" Republican Senator Olympia Snow after she threw in the towel and announced her retirement), the overall line-up in the next Senate will be 55-45. Even without the self-destruction of two Tea Party Republican candidates who proved to be too extremist even for heavily Republican states, Todd Akin in Missouri and Richard Mourdock in Indiana, the Democrats would still have wound up with a 53-47 majority in the Senate.
But there is one conspicuous anomaly in this overall picture. The Republicans went into the election with a 240-190 majority in the House of Representatives (the 2010 elections gave them a 242-193 majority, but since then 5 seats had become vacant), and they will wind up with a slightly reduced but still solid majority in the next Congress, probably 236-199. [Update 11/12/2012: Depending on the outcome of 5 races where votes are still being counted, the Republican majority could be whittled down to 234-201.] Understandably enough, House Republicans claim (in effect) that the voters have given them a mandate to persevere with their previous strategy of all-out obstructionism, hyper-partisan intransigence, unwillingness to compromise, and immovable refusal to consider returning tax rates for the top 1-2% to Clinton-era levels.
So how and why did the Republicans wind up with a probable 37-seat majority in the House? Well, part of the explanation must lie split-ticket voting—that is, some people voted Democratic in the presidential race but Republican in their House district race. But that factor alone can't really explain the results, because if one looks at the national vote totals, the House Republicans actually lost the overall popular vote by about 500,000 votes. As Ezra Klein observes, "That’s a close election — 48.8%-48.5% — but it’s still a popular vote win for the Democrats."
The really critical factor was a different one: gerrymandering. The Republicans did an outstandingly effective job of gerrymandering House districts in states they controlled. And the electoral timing was lucky for them. The 2010 mid-term elections went very well for the Republicans across the country, giving them control of a lot of state governments. And the 2010 census provided the occasion for redistricting Congressional seats, so the Republicans took the opportunity to do that in ways that maximized their partisan advantage.
No doubt the Democrats would have done something similar, if they had gotten the opportunity to do more of the redistricting after the 2010 census. That's the way the game is played, like it or not (which we shouldn't). So the Republicans do have a House majority that they won playing by the rules (even if they stretched them to the limit in some states). That's very unfortunate from the perspective of the public interest, but so it goes.
However, when the House Republicans and their propagandists claim that they have received a popular mandate to continue sabotaging the economic recovery, protecting the wealthy from Clinton-era tax rates, manufacturing artificial debt-ceiling crises that recklessly take the country to the brink of fiscal disaster, and so on ... then none of us should take that claim very seriously. The Republicans took that program to the voters in three different arenas—the elections for President, for the Senate, and for the House—and in all three most voters wound up voting against them.
Yours for reality-based discourse,
P.S. (11/14/2012): It does seem clear that post-2010 gerrymandering was a key factor in explaining how Republicans kept their House majority despite losing the overall popular vote; but it was probably not the only factor. And it's worth mentioning that some skeptical analyses have tried to downplay the significance of Republican gerrymandering in this connection. For example, Eric McGhee ran the numbers and concluded that, at most, post-2010 redistricting can account for only half of the difference between the Democrats' proportion of the popular vote in House races (about 50.5%) and their proportion of the incoming House seats (about 46%). Maybe, maybe not. But even if we grant that, we would still be talking about half of the Republicans' House majority.