Any theoretical or actual limits are irrelevant. What counts is the practical limits of the image viewable by most monitors are.
What station_two said - depending on what an image is used for, neither the dimensions nor the file size may matter that much, but of course it doesn't make much sense to create a 4000x3000 pixel image for a mobile web site just as it doesn't make sense to make such an image a high-quality JPEG that will be 4 MB or so in file size because it will take forever to load. Whatever. This topic is much more complex than telling you some absolute values and if you have no feel for things, you might wanna spend some time surfing some reference web pages...
I am wondering, if the OP was refering to the warning dialog box about the file size maybe too large for save for web. Or did they do away with that warning?