If you have generated your UV map and have exported that from Maya at the resolution you want, then you should not get any issues here the texture i too big. From the sound of it I think you may be doing what a lot of people do in the begining and just apply textures to faces using a planer, or auto Projection.
Really you need to do the Auto Projection and then head to the UV Editor and get all the UV's layed out as you need or want them, once thats done then you export the uv layout to a good image format and start working on it from there in Photoshop. You are correct in the fact that the higher res the better (as long as your pc can deal with it). Hi-Res textures can cause Maya to slow down considerably or even crash out.
Can you post a screenshot of what your result is and deatil how you did it that way we can better advise you on where to go next.
Chris (formerly R@nSiD)
When the power of love overcomes the love of power the world will truely know peace - Jimmy Hendrix
Winner SM VFX Challenge 1
3rd Place SM SteamPunk Challenge (May 2007)