"For example, does the deficit required increase if your weight stays the same or you lose weight more slowly than expected?"
No, it does not.
"Or, is it the goal date that shifts instead?"
Yes, the goal date will update based on your weight inputs and the calorie deficit that you selected.
Now, what Fitbit does update is your calorie burn, based on your weight inputs (much to my chagrin). If you lose weight, for example, you will burn fewer calories for a given level of activity. Maintaining a given deficit means that over time, the amount of food you can eat will decrease. In my case (40lb later) I'm burning almost 500 fewer calories every day, despite similar levels of exercise and activity.
I would recommend giving things a few weeks before trying to adjust your deficit up or down. Make sure you wear your fitbit consistently, log everything you eat as accurately as you can, and try to weigh yourself under consistent conditions each time. After a few weeks you can look at your weight trendline (because you'll have day-to-day fluctuations based on water intake, bathroom visits, etc) and see if it's matching what you expect.
If you're good with math and excel you can even pull the .csv reports, add up calorie intake and expenditure, and use the weight figures to see how far off you are. In my case, I found that on average I'm off by about 150 calories a day--either I'm burning a little less than the Fitbit says, or I'm missing a bit when I log things. But now I know that and then I can compensate for it.
I just wish there were a way to manually input a target deficit instead of selecting from the list.
