We've got a 1/2 inch gap between our bathtub faucet and the tile, and as you can imagine water has been leaking through and sometimes even dripping though the wall to the floor below. The tile is starting to wear out and chip off as well, so I'm not sure if caulking will hold or even work for such a large gap. We are saving up for a bathroom reno but need some sort of solution to hold us over for the next few months at least.
That is too large of a gap to seal with caulk. If you are looking for a (very) temporary solution you would be better off with plumber's putty. Get a tub of putty (it is not expensive) and knead it well until it is warm and soft, then pack the void with it. It should do a fair job of keeping the water out for awhile, until a proper repair can be completed.
Proper repair would be removing the tub spout and properly sizing the pipe so the spout was close to the tile, then caulk.