Charles Helliwell's Answer:
Don't blame yourself, Kathy. It's something we ALL do from time-to-time.
This is a mistake, which is yours to be rectified, and fortunately, you have both the time and the opportunity to exercise that prerogative. The guilt you feel is not directed towards the employee; it's directed at you, and that's fine. You should feel guilty and responsible for lacking diligence in this matter, and one thing's for sure, you won't make this mistake again, will you ?
Put all feelings and emotions aside here and address this in terms of performance, productivity, integrity and honesty. That's what a probationary period of work is there to uncover or validate, and it sounds as if this particular employee has failed on every count.
It's just as hard, sometimes, to admit that you are as much at fault as a bad hire. However, being a responsible and diligent manager is all part of the job and something you'll have to learn to deal with, no matter how painful it might be. This won't be the first time, or the last.
So deal with it; take your medicine and move on. Failure to do so will only prolong the inevitable and may well result in your termination as well.