Yes, Cruz had demonstrated that amply by refusing to apologize or take other remedial action.
Refusing to apologize for a misstep is a sign of immaturity and hubris. I fear that is shows Cruz does not have the temperment to be a chief executive.
Combine the mailer with his fake oath of office with Beck. That was really poor taste and a denegration of the oath. I wonder if Ted would take a fake wedding oath, and how his wife would feel about that.