In my experience, the effort invested in testing will vary considerably based on the complexity of the software you're testing, whether your test materials are prepared already, the difficulty of recruiting participants and the number of personas you feel you need to text.
Complexity of Software - I tested an Internet Bill Pay / Banking app in 1996 when that sort of transaction was complex for many users. Consequently, they moved slowly through the app and it was easy to consume an entire session simply testing view account balance and transfer funds. More sessions were needed to test add payee, confirm payment was successful, dispute payment, etc
Effort Required to Produce Test Materials - Are you testing an existing app, paper prototypes, or an interactive prototype? The more you need to produce, obviously, the bigger the effort. In my experience, this is the largest variable that affects project duration.
Difficulty of Recruiting Participants - I'm currently testing an app (more LeanUX than usability but still relevant to this question) that has ~200 possible users nationwide. Each controls around $2 billion in spending annually. Getting their time has proven to be very difficult. Can anyone off the street be a test subject, or do you need to invest significant time recruiting test subjects with unique qualities?
Number of Personas - If you're testing 6 distinct personas, obviously this is much more time consuming than 2. It tends have a multiplying effect on the other aspects of testing - more personas often requires more screens in the prototype, more effort in recruiting and is an indicator of software complexity.
I can't tell you how to estimate the effort. But I can suggest an approach that's worked for me in the past. Borrow a trick from Agile software development and timebox. Tell management that you want to test 1 persona using simple paper prototypes of one particular feature. Test five participants and promise you'll get it done in 40 hours (this assumes that recruiting participants is relatively easy). Odds are you'll get the task done pretty close to the limit given to you. This allows you to return to management with a) some interesting results on how the app can be improved and b) a much better handle on what it takes to do usability testing with your team and your users on your app. This tends to make subsequent decisions easier and increases comfort levels with approving larger testing efforts.