I found this dubious, so I went googling. I felt I ought to share what I found:
http://www.benzinga.com/general/politics/14/11/5012697/why-m...
http://www.huffingtonpost.com/2011/02/01/meg-whitman-outspen...
I only say "the corporations" as those entities who attempt to participate in the gift economy laid out in Lessig's "Republic Lost." I do not think a meta trade group reminiscent of ALEC or the Chamber of Commerce would be very unlikely if there was evidence that this strategy was effective.
While i agree with your point about swaying voters, as well as what i've read about Levitt's work on the subject, with the assent of self-selective media, Fox News and other various media outlets of questionable independence, it seems that there is much influence in coordinating talking points than there is in ads alone. Maybe i'm a bit paranoid about that, but with the deterioration of a diversity of media firms, i really don't think so.
The issue about billions of good money available amounts seems to lack the reason there is so much spending. The opportunity cost of a coal firm fighting potential crippling regulations would be essentially zero. If they stand to loose significantly in certain elections, then they can clearly spend exactly an equal amount to stop it.
On the side of good, there are no hard and fast numbers to budget, thus an coordination problem arises on who ought to spend what.
Like i said before though, i think lack of knowledge of the effectiveness of such an organization is it's greatest asset. If politicians are suddenly hit with a big stick, they may be out for the count. If they know what they are up against, they can probably raise money to counter-counter accordingly.
The free-speech stuff in elections is a bit of a black hole.
One mans free-speech is another mans boogeyman.
Likewise, the issue with corporate personhood.
But fighting non-profits would be a social win and is on firmer logical ground.
Just food for thought.
You say "the corporations" as if it's some secret cabal. Most spending is done by trade associations, not corporations directly. Trade associations like to get their legislation through. But they don't run the show.
Money only matters to the extent that it buys ads that move voters. And there's only a limited amount that matters in an election. If you take a house race and outspend your opponent $10 Billion to $1 Billion, but have a worse message, you will lose.
The total cost of the all federal elections in 2012, including the presidential, was around $8 billion dollars. That's a big number. It's almost a billion dollars more than the worldwide market for adult diapers:
http://online.wsj.com/articles/as-births-slow-p-g-turns-to-a...
It's a very small number compared to our economy. There's enough good money out there to run our elections cleanly. We just need the will to do it.
CounterPAC is a hack to do that without waiting for congress to act. You can be for it or against it, but it isn't fluff.