We were dealing with this issue today when attempting to save a rather large project schedule.  The project would create the getting queued message in the queue them immediately fail.  We knew that meant the information from the Project Client was not reaching to the Server. That made us think that issue is related to Project Local cache.  Unfortunately after deleting the project cache the issue persisted. 

When reviewing the logs there was very little information being generated.  Under closer examination were noticed the following error “The attempted operation is prohibited because it exceeds the list view threshold enforced by the administrator”.  For an on-premise instance of Project Server you are able to adjust list view threshold limit.  In SharePoint online you are limited to 5000.  Steps to adjust are below:

  1. Navigate to Central Administration. You can get to it by going to the SharePoint server and searching for “Central Administration” under the start menu.
  2. Go to Application Management > Manage Web Application and click on your web application to select it.
  3. In the Ribbon, click on General Settings drop down and choose “Resource Throttling”.
  4. In the “List View Threshold”, increase the value and click OK.
  5. Check the list now. Keep increasing the threshold if the error persists.

Once we increased this value our project was able to save successfully