REP holders can choose to do no work (though they won't receive fees) or they can do some work and receive fees (proportionate to how much REP they stake on that work).
Work is divided up per REP holder, not per amount of REP. Having a larger share doesn't mean you will have to do more work. It is best to not think of REP as a labor token but instead as a security token. A small amount of work is required to apply your security, but the labor isn't really what is being paid for.
As to how much work is required, it all depends on how smoothly things are running. If everything is running perfectly smooth then there will be very minimal work required because all (or almost all) markets will resolve accurately in the self-reporting phase. In this case, REP holders will simply need to show-up once a month in the UI, click a few buttons, sign a transaction, and then come back a month later.
If things are not running smooth then the amount of work is bounded only by the number of markets there are, where reporters will need to do some amount of work for every market (research correct outcome).