You were right to be careful and go slow. Bottom bracket threading is very fine and it's VERY EASY to cross thread one if you're not careful.

Sometimes though, the threads on the BB are lousy and you have to give it some force. Try installing the old BB again. Does it go in smoothly? If so, your frame is fine. When installing the new BB, be absolutely sure you have it on straight, then give it the force required to tighten it up.

Sorry to mostly repeat what HillRider said, my main point is to avoid cross-threading the BB.