Of course, after 20 or more years of constant, and often disingenous, agitprop from the abolitionists, on a wide front including the churches, the media, and the "academy," one would expect that public support would be affected.
What's really of note, then, is that public support has remained fairly level despite the intense abolitionist campaign. The real bad news for the abolitionists is that support for the death penalty is probably greater than thought: Sharp notes that when asked about particular cases, support for the death penalty shoots up:
81% of the American people supported the execution of Timothy McVeigh, with only 16% opposed. "(T)his view appears to be the consensus of all major groups in society, including men, women, whites, nonwhites, "liberals" and "conservatives." (Gallup 5/2/01). 85% of Connecticut respondents voiced support for serial/rapist murderer Michael Ross' "voluntary" execution. (Quinnipiac University Poll, January 12, 2005).
Most tellingly, some people who voice general disapproval of the death penalty actually support it in certain individual cases, such as McVeigh, or for terrorists.
This suggests that public support for the death penalty is actually quite more robust than the answers to the general "do you support the death penalty or life without parole" question would indicate.
No doubt the anti-capital punishment folks will soldier on despite their lack of success.