According to this ABC piece, it did: "...the country appears to be revisiting its stance on the death penalty, in light of Troy Davis' execution last week."
Readers of this blog will not be surprised to learn that the story adduces no evidence to support this statement. It's simply an article of faith in some quarters that Event X or Study Y always "re-ignites questions about capital punishment," or some such thing. For example, the title of every article I have ever seen on the DPIC site is roughly, "New survey shows declining support for the death penalty." I have yet to see a single one that says, "New survey shows increasing support for the death penalty," even though DP support has remained stable or shown occasional slight increases over the last seven or eight years.
Still, given all the massively slanted coverage of the Davis case, it's a fair enough question. Did his execution decrease DP support?
Well, there's a way to find out: Ask. While such an enterprise was apparently too much for ABC, it was not too much for the quite reliable pollster Rasmussen. The topic sentence of his report is, "The execution of Troy Davis last week for murdering a Georgia policeman prompted controversy here and abroad, but it did little to shift opinions on the death penalty." Specifically, he finds that support had previously been at between 61%-63%, and is now at 60%, a statistically insignificant difference. And in Rasmussen, as in every other poll I've seen, DP support remains at better than 2-1.