If you've ever put your foot in your mouth, you've probably said something impolitic. If you have made an impolitic statement, it was a politically unwise one.
It is impolitic to fail to remember flowers for your beloved on Valentine's Day, or to fail to show up in class when your grade point average is hanging by a thread. Remember back in 1981 when then U.S. Secretary of State Alexander Haig informed the press after the assassination attempt on President Reagan that "I am in control here?" Well that was a classic impolitic statement. Poor guy resigned the following year.