Julie -
I believe it is absolutely achievable, but in my humble opinion, plus my experience in doing this off and on over the last few years (mostly off), you have to have a solid business plan and you have to have a plan that goes beyond more than JUST having clients.
I'm only speaking from my own experience, where most of the reason there has been the mostly "off" scenario is because I didn't plan nor have a vision of how I would expand and also in planning to have mulitple streams of income.
I'm sure there are more experienced veteran VA's on here that may have better suggestions. I'm coming from the perspective of being one who did fail a couple of times...I was told what I needed to do before but I didn't give myself time to plan properly and to have a plan for more than just supporting clients. In other words, don't follow my example. I didn't listen to a lot of people who coached me, mentored me, and I even ignored a lot of the advice on this forum!
I'm coming from the perspective of learn from my mistakes so you won't be like I was.

This time IS my last time around. I believe that I have grown, learned, and finally got a lot of sense knocked into me - and if my failures help someone else succeed, then that's a GOOOD thing.
As far as getting clients...or anything else...guard against letting yourself become overwhelmed. Becoming overwhelmed will only hold you back. The old saying about "slow and steady wins the race" is so true. Approach your business like any project. Start with the end goal in mind and then back into it, breaking up the steps to get there, refining them further and further, breaking them down into smaller and smaller parts, and then get your schedule and task lists together and then stick to that plan.
Don't let yourself get sidetracked. This has been my BIGGEST mistake! You can always refine your plan, expand, add more offerings, etc. - but when these wonderful people on this forum say determine your niche - determine your niche.
I for one am happy to help anyone in any way that I can. Lord knows that many, many have helped me and so it is an honor when I can help another. So feel free to get in touch anytime. I don't know as much as many - yet...but am happy to share what I do know.