The query that we use to generate Due issues is like this:

http://localhost:8080/jira/secure/IssueNavigator.jspa?reset=true&jqlQuery=project+%3D+HSP+AND+resolution+%3D+Unresolved+ORDER+BY+due+ASC%2C+priority+DESC%2C+created+ASC&mode=hide

It would make sense to add 'AND due is not empty' to the query so that we do not include issues that have no due date set on them.