Actually ...
I think that broadening and deepening together will be a matter of survival for most IT consultants in the future. Marty built on some of my earlier points by being more specific.
Yes, you're quite that right in that it's impossible to know absolutely everything even about a single domain. My main message is that to be a successful IT consultant, you should strive to be a "versatilist". In other words, become specialized in one area and apply your transferable skills to another related area.
Although my current experience lies in healthcare, I have a strong background in financial services which includes 3 banks. Right now, I'm being considered for a contract with a supplier of personal health insurance, which I see a combination (or middle ground) of healthcare and financial services. Pushing my expertise in both industries may help me win the contract.