It seems obvious that they did. He outspent Gingrich 5-1 precisely when his poll numbers were increasing. But, as is well-known in social science, conclusively demonstrating the effects of campaign ads or other media is actually quite difficult.
Thanks to some data that SurveyUSA was willing to provide me, I took a stab in this new post at 538. The conclusions are certainly not ironclad, but maybe they constitute a baby step.
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