With what granularity can you specify photo size (in mb's), if at all, in a standard digital camera?

Most any camera that allows you to adjust anything, allow you to adjust resolution, not megabytes. Adjusting the resolution does have an effect on those MB, higher resolutions requiring more of them.

Then you throw JPEG compression into the mix. Each photo taken will have exactly the same number of pixels recorded at the sensor, but the compression engine will discard more or less for each specific shot, depending on what is there. This means that file size is variable. As an example, my Canon 30D stores photos (using fine JPG setting) at anything from about 2.5 to 5 MB, with the average about 3.5 MB. My Sony A300 has a few more pixels on the sensor, so the file sizes are slightly larger, but not by much. Most point and shoot style digital cameras compress their photos even more than the DSLR cameras... with resulting smaller files for the same number of pixels on the sensor.