Our Jenkins installation has over 75K jobs and about 1600 views. Upon upgrading the dropdown views tabbar plugin from 1.6 to 1.7, any attempt to retrieve the contents of a view through the web UI would hang. The attached stack trace is from a thread dump of Jenkins while trying to get the contents of a view by just visiting the main page. Other operations within Jenkins, such as going directly to a job or build or to the configuration interface work fine. We observe this behavior with or without the option to show job counts. We also verified that we see the same behavior with 1.625.3 and 2.0-alpha 2.
I'm not sure what other information you need or if there are things we should try. With a relatively low amount of effort, it is possible for us to spin up a test copy of our production environment for further testing.