I have a Next PX 6.0 mountain bike that I bought at Walmart a few years ago. It did not come with pre-installed mounting screws and/or threads for a bottle cage. The frame has large, strangely shaped tubes (oval-ish is perhaps the best way to put it), so many attachments that come with bottle cages also don't work as they are not big enough to wrap around the entire tube. My current configuration is with cable ties, but they keep breaking.
It might be hard to tell, but the bottle cage is currently only attached by one cable tie, as the other two have snapped off. (The bike is hanging from the ceiling, which is why the orientation might look off.)
Are there any options out there for a more permanent installation of a bottle cage?
[EDIT/UPDATE: I gave this bike away when I graduated from college last year, which was before I got around to attempting any of the solutions offered here. If you're in a situation like I was, I'd say that the answers/comments that I was given should help you figure out how to the solve the problem.]