I have been on both sides of this situation, as an employee in a consulting firm in the telecommunications industry (in the United States) and later as a project manager in the same firm.
The simple fact is if you do not have an employment contract (and in my experience they aren't common in the US) or are a member of a union with a contract with the company, you are considered an "at-will" employee, which means they can terminate you for any reason they want with or without notice (and likewise you can leave of your own accord for any reason with or without notice).
So the fact that you don't have a project and they don't want to pay you any longer to do nothing, is entirely legal. I've face this situation as an employee and fortunately something always came up, so I never managed to get laid off, however, there were times it was very close. I've had times where it was strongly encouraged that I take some of my banked vacation time for a week or 2 so they had a little time to find a new project for me. But I was never asked to work "for free" during a period of time.
And on the flip side, I've face this situation as a project manager in dealing with my own employees. It was a decision that I never enjoyed making and tried to find something, but it was necessary to ensure projects and overhead spending never went over budget. I've never asked anyone to work for free either, so the fact that they did so is quite unusual in my experience (and depending on the locale, may not even be legal, although I'm not a lawyer, so take this with a grain of salt).
Many times companies of this nature, while being profitable, live "invoice-to-invoice". Often they simply do not have cash around to pay people when they aren't actively working on a project and making money. Depending on your exact line of work and your exact skills, upper management may see you are easily replaceable because they know if they let you go and a project comes up requiring your skill set, they can rehire you or find someone else with similar skills quickly. It is the unfortunate fact of working in the consulting industry.
From the medical insurance side, Joe's answer really hits everything. they are required by law to offer you COBRA coverage so you can maintain your current insurance, but you have to pay the premiums. The Affordable Care Act may also you options to get insurance coverage on your own.
So in short, the best advice I can offer you is start working your contacts. When projects get close to the end and there doesn't seem to be another coming up, always started putting feelers out.
I left this company over a year ago (for my dream job) but I still get contacted by recruiters looking for people with my skillset, so I always try to refer friends that I know are looking. that is why it is wise to keep in touch with everyone you have worked with in the past (former clients, managers, co-workers, and even people you have supervised) as well as recruits you have run into, and check in with them regularly. You never know who might be looking.