Hmmmm... based on your comments, it sounds like you either place WAY too much emphasis on settling, or not enough. I don't know if this is happening to you, but... If Civs make demands during the early game (e.g. "Give me X gold as tribute"), it's often better, in the long run, to simply give them what they want (within reason, of course). Return at a later date to grind them into dust. I know that was a big mental block for me... and it resulted in a lot of early wars I couldn't afford to fight. While rapid expansion is the key, do what you can to maintain somewhat of a military presence. Focus on offensive units as opposed to defensive units.
A breakthrough might not be necessary. Simply grabbing, and holding, a handful of cities might do the trick. Set realistic strategic objectives, and go for them with single-minded zeal. Sue for peace when you're happy with your gains. Rest, relax and reformulate. When the time comes, engage in another limited war w/ the objective of siezing key resources/cities/luxes. Basically: grind down your opponents bit by bit, until you can afford to engage in a full scale war of conquest. Sooner or later you will achieve the breathing room that you want -- hopefully.
-V