The length of latus rectum of the parabola whose focus is $(3,3)$ and directrix is $3 x-4 y-2=0$ is ______ units.

Finding the latus rectum length requires determining the focus-to-directrix distance. Given focus $S(3, 3)$ and directrix $3x - 4y - 2 = 0$, this distance is calculated as:

$d = \frac{|3(3) - 4(3) - 2|}{\sqrt{3^2 + (-4)^2}} = \frac{5}{5} = 1$

For parabolas, the focus-to-directrix distance equals $2a$, where $a$ represents the focal length. Thus $2a = 1$.

The latus rectum length is given by $4a = 2 \times (2a) = 2 \times 1 = 2$ units.

Comparing with the options, the correct choice is $\boxed{\text{D}}$.