The life of a contractor is very tough to say the least. Why corporations do it is beyond me because with NO notice, you could quit and pretty much leave that operation high & dry.
In terms of unemployment, there's nothing you can do because you're not employed by either the company or the contracting firm. You're pretty much there on a day-to-day basis on financial terms. Depending on the type of contracting you're doing, you may apply for unemployment compensation from the contracting firm depending on the terms you agreed upon.
You can tell from your paycheck - if you take out your own taxes, you're on the harder type of contracting. If someone else takes them out, you can probably collect from them. If it's the second case, don't tell them something's going wrong, even though they'll tell you they'll be willing to find you work. It's a ploy so you won't collect, but that's another story.
As for your work situation, be frank with your boss and ask about your options. With a merger, he's looking after his behind, so he might be doing your job if push comes to shove.
You also have to take his advice with a grain of salt. He doesn't want to make his division look bad, and it sounds like things would be problematic for a while if you left suddenly. He may give intentions one way, but act on another when time comes.
Look for possible work now, hopefully you'll find something if things do not work out at the current place. If things look good in terms of possible employment, take the opportunity and look at all of your options.
Finally, I know in your mind you probably don't see the difference between contractor and employee, but in the grander sense of things, if you were an employee, the company would have to show your loss on their taxes. This is something investors are wary of and that event is something they will have to explain to them.