Initially I thought you were correct, but September Labor Day actually predates the Haymarket affair by four years.
"The first big Labor Day in the United States was observed on September 5, 1882, by the Central Labor Union of New York."http://en.wikipedia.org/wiki/Labor_Day
You're right. Thanks for the correction! It does look like Red-phobia played a role in keeping the September date, but it was trade unions that chose it initially.
"The first big Labor Day in the United States was observed on September 5, 1882, by the Central Labor Union of New York." http://en.wikipedia.org/wiki/Labor_Day