Despite being set as an Administrator and Project Lead, I only see myself and "Administrator" as options for assigning tasks.
I would check Administration --> Issues --> Misc Schemes --> Permission Schemes --> Default Permission Scheme and see who you have set as "Assignable Users" under Issue Permissions.
Do you mean that you are not seeing anyone in the assignee dropdown? Do they have Assignable permission set?
http://confluence.atlassian.com/display/JIRA/Managing+Project+Permissions
It looks like the User has to be in Jira-Developer Group to be assignable not just a Jira-User. Once I added User to this Group I could assign a task even though the person is not a 'Developer'
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