Tea Partiers would see Thomas as one of their own ... Wall Street Republicans would be buoyed by Thomas’s opposition to environmental regulation and his free market philosophy. Blue-collar workers could embrace Thomas’s up-by-his-bootstraps story of rising from incredible poverty ... Evangelicals will like that he’s against abortion, gay rights, and limits on prayer in school.
Winkler says that Thomas would have to resign from the Court to run, but it's not clear why that must be so. It's not in the Constitution that a Justice cannot pursue elective office.
Thomas has made no indication he is interested in the presidency.