Stuart, if you negatively offset the consumer confidence series by a certain duration, you may find a higher correlation.  Energy price statistics are reported in real-time with respect to the underlying phenomena.  However, consumer confidence is based upon a survey that incorporates recent consumer experiences.  Could you experiment with various offsets in the range of 8-16 weeks?
Good Point.
That is what came to my mind as well when I first looked at this data.  How do you make sure the data corresponds to the same time period?  Likely one will need to be shifted in time relative to the other - you'll likely need your militant empiricist skills to figure it out.  Beyond just a simple time shift, one set of data may be averaged more than the other as well, which I think should reduce the correlation.
I would bet 8-12 weeks from eyeballing it - but could be an illusion as the human eye likes to find correlations!
This is a great exercise in critical thinking and statistical literacy. The newspaper reports assert a strong correlation and Stuart brilliantly went out and tested it. Refinement of the methodology is a great idea, but you can eyeball the long-range chart and see that there appear to be good grounds to doubt that there's a strong correlation between gas prices and consumer sentiment. And of course there is, as the employment outlook, generally perceived state of the economy, income growth (whether wage or refi based), and so on weigh in heavily.

But here's a tongue in cheek prediction: if it's a cold and "peaky" December,  the major influence on the subsequent consumer confidence stat will be the number of times "I'm Dreaming of a White Christmas" get played at WalMart.

Actually my comment with regard to offset time series is more appropriate for situation in which the relative changes in the values are compared, as opposed to your comment above comparing their absolute levels.  It's plausible that consumers become habituated to energy price levels over time, and that only relative changes (in particular sharp increases or sharp decreases) affect their responses to the monthly consumer confidence survey:

http://www.conference-board.org/economics/methodology.cfm