Exporting webform information programmatically I have a Drupal site that uses the Webform module. It has many options for downloading the results via the Drupal interface but it doesn't have anything out the box to get the data programmatically (JSON ect). 

Is this possible? Authentication will still be require i.e only Drupal users for the site should be able to access this information via the JSON request.
You might have to create your own.
It would probably be worth submitting back as a new module too.

All you would have to do is implement hook_menu() to add your menu callback.
In hook menu you can set access arguments to make sure no one case use it unless they have a particular permission.

You can add your own custom permission using hook_permission().

Then the callback function could use webform_get_submissions() to load the submissions for a given webform and return them using drupal_json_output()

You could pass in a webform nid argument either via the url, using something like 'get-webform-submissions-json/%node' as your menu path, which would automatically validate the nid and load the node for you. For more information on that see http://drupal.org/node/224170
You could also just pass it in as a query parameter and use $_GET['nid'] in your callback function, however then you need to validate it yourself.