The identity manager needs to do a POST to login to access your webmap. Since you're hitting arcgis.com, this is a cross domain request so you need to do this via a [proxy][1]. Have you set up a proxy for your app?

Looking at the docs, this isn't clear. We'll update our documentation to say you need to use a proxy if you want to use a private webmap in an app you host yourself (if you haven't guessed, I work on the JS API team).

  [1]: http://help.arcgis.com/en/webapi/javascript/arcgis/help/jshelp/ags_proxy.htm