From my experience, the length of time to feed a new package or nucleus depends on the time of year, ie: weather, not on how long you have had the nuc. At my latitude, we generally install nucs sometime during the first two weeks of May. I wouldn`t dare feed them for more than 10 days or so, for the reasons already outlined above by Finsky and others.
The Queen could become honey-bound with unnecessary syrup thereby encouraging swarming. You can also contaminate your honey with sugar. At this time of year, there should be plenty of nectar available to our bees just about everywhere in North America. However, your experience in the deep south may be entirely different.
Where I am situated, in the Ottawa River valley, it is hot (31 C. or 88 F.), humid and we are in the middle of a heavy honey flow from wild honeysuckle, lilacs and late spring flowers and fruit tree blossoms.
Another point is that we consistently get some surplus honey from newly installed nucs, with enough left over for the bees to overwinter comfortably in our extreme conditions.