You'll want to read John Sides on the David Brooks column about money in politics. As John says, Brooks is correct to say that people overrate the importance of money in elections -- but John corrects him on the current debate over spending effects: "the major debate is not over whether money matters, it's over the relative impact of incumbent and challenger spending." The people who study this (and I'll repeat John's citation of Gary Jacobson) most definitely do believe that campaign spending matters -- but not as much as some think.
Why does money have only limited importance? It turns out that there are two major factors on individual vote in Congressional elections, and then various small factors. For one of the major factors, partisanship, campaign spending doesn't matter at all: no one sees a bunch of ads and switches from being a Democrat to being a Republican. Since House districts often have overwhelming partisan majorities, party voting alone explains the outcome of most House elections. Spending also matters little to some of the small factors, such as presidential approval and the condition of the economy.
The reason campaign spending does matter is the other major factor. It turns out that if you ask people what they think about the two candidates, and note the balance of things they say that they like and dislike about each, that the combination of that is a good indication of how they'll vote. Not too surprising, right? If I can think of three things I like about the incumbent, and nothing at all about the challenger, of course I'm more likely to vote for the incumbent. In fact, that's how the incumbency advantage actually works -- over time, constituents tend to learn a couple of positive things about the local Member of Congress and (assuming no scandals) nothing negative, while they usually have barely heard of the challenger. Again, party matters: many of us will still vote for a challenger from our party even in the face of that situation. These are all tendencies, not absolutes.
Money, of course, helps candidates "teach" us to learn good things about them and lousy things about their opponents. The most obvious point, as John Sides quoted Jacobson as saying, is that a challenger who doesn't spend much money and has no other means of getting the word out will have no chance to win. It's a little different for incumbents, however. Incumbents do all sorts of things in the course of fulfilling their official duties -- casework, district projects, meeting with constituents, local media hits. A surprising number of voters will actually have had either a direct positive experience with a long-term Member of Congress, or know of someone who has had a positive experience. By the time a multi-term incumbent gets to the 2010 election, it's not clear how much a bunch of TV ads will add to all of that. More generally, campaigns and campaign spending are only one of the things that affect how we feel about the candidates, which (remember) is only one factor in determining how we vote.
So money matters. It just matters in limited ways.