The answer, it seems, is yes. In a 2001 survey conducted by Mark Peffley and Jon Hurwitz, a random subset of whites was asked:
“Do you favor or oppose the death penalty for persons convicted of murder?”
Somewhat favor: 29%
Strongly favor: 36%
Another random subset of whites was asked:
“Some people say that the death penalty is unfair because most of the people who are executed are African-Americans. Do you favor or oppose the death penalty for persons convicted of murder?”
Somewhat favor: 25%
Strongly favor: 52%
That is a 12-point increase in overall support. There is much more to Peffley and Hurwitz’s analysis:
bq. Although there exists a large and well-documented “race gap” between whites and blacks in their support for the death penalty, we know relatively little about the nature of these differences and how the races respond to various arguments against the penalty. To explore such differences, we embedded an experiment in a national survey in which respondents are randomly assigned to one of several argument conditions. We find that African Americans are more responsive to argument frames that are both racial (i.e., the death penalty is unfair because most of the people who are executed are black) and nonracial (i.e., too many innocent people are being executed) than are whites, who are highly resistant to persuasion and, in the case of the racial argument, actually become more supportive of the death penalty upon learning that it discriminates against blacks. These interracial differences in response to the framing of arguments against the death penalty can be explained, in part, by the degree to which people attribute the causes of black criminality to either dispositional or systemic forces (i.e., the racial biases of the criminal justice system).
Find the paper here.