What could cause the Features create page to time out?
The features UI can be notoriously slow for large Drupal sites. We recently experienced a ~50 second delay in loading the aforementioned page (create a new feature). The reason why (after debugging it all) was it was loading every single menu item on the site (>3000 of them) and trying to render a checkbox for every single one.

I posted a simple workaround on drupal.org https://drupal.org/node/1153028 - it looks like my patch will never get accepted in features, but at least it got the module maintainers looking at the performance issue.

On a related note, you do not need to use the GUI in order to create a feature. With large Drupal sites I would recommend using drush only as it has the advantage of being much faster. Please see https://drupal.org/node/960926 for more details.