Yesterday I tweeted:
Will the reality-based community vocally embrace the repeated finding that money has little influence in U.S. politics? 
The link is to Tyler’s discussion of a great lit review on money in politics.  Levitt has another good lit review with more focus on money in elections per se. 

Here’s my idiosyncratic lit review: In recent studies using a variety of methodologies, it’s rare to find evidence that money buys elections (my GMU colleague Thomas Stratmann finds an interesting exception here; the paper won the Duncan Black prize at Public Choice).  
In the olden days, scientists knew that money didn’t noticeably matter for incumbents: If incumbents won or lost it wasn’t because of differences in campaign spending.  But in crude regressions, it looked like money mattered for challengers. Now, with fancier regressions, it appears money matters little for challengers as well, especially in well-studied, data-heavy House elections. 
The old results were driven by omitted variables: Weak incumbents drew in stronger challengers, and hence more challenger cash.  The challenger cash was a sign of the challenger’s relative strength, not much of a cause of her relative strength.  
Yale’s Alan Gerber reports some field experiments on campaign finance here; he finds evidence that extra money mattered for challengers but not for incumbents.  However, one might want to read the results cautiously: after all, the campaigns involved in the field experiments apparently had a Yale political science professor as an unpaid consultant.  I suspect that’s worth quite a bit.  
Short version: Too many multi-millionaires lose. 
But conventional wisdom, especially among progressives, is that money can buy elections. The Citizens United case was supposed to be the end of democracy since it meant unlimited corporate spending on elections.  If money really did buy office, 2012 should have been great evidence for the hypothesis.  
Instead 2012 looks like a case study in the powerlessness of money, in the triumph of the autonomous voter.  For instance, the Sunlight Foundation reports that 2/3 of outside cash was spent on losers.  Seems to fit the conclusion of Levitt’s 1995 lit review: 
It seems unlikely that campaign finance reform, at least in its current guise, will have much impact on the functioning of the American political system…In the light of that conclusion, the substantial amount of energy devoted to the topic by the public, the media, and politicians might be more productively channeled towards other issues.

In a better world, we’d have spent the last week celebrating the newfound evidence that money does little to buy elections. 

Coda: Levitt’s review is a good, low-tech read. You really just want to read pages 188-192 of this PDF; and here’s Freaknomics coverage of campaign finance from earlier this year.