**Yes, there is a minimum dosage.**

From "Harry Potter and the Deathly Hallows", Chapter Twenty-Five, "Shell Cottage":

> There was problem after problem to overcome, not least of which was that their store of Polyjuice Potion was greatly depleted.
>
> 'There's really only enough left for one of us,' said Hermione, tilting the thick mud-like Potion against the lamplight.

As for the exact amount required, that isn't made clear in either the movies or the books.  The closest there is to any mention of a specific dosage is in Chamber of Secrets (Chapter Twelve) where they each take a "large dollop" of potion.