Companies can "promise" anything they want, but unless you get it in writing in a legally binding form, like a contract, it's not worth anything. If conditions deteriorate, they will have to lay off again. At best you'll get a "I'm sorry this had to happen. I know I said it wouldn't last week/last month/last year...". To be fair, sometimes the managers themselves get laid off too, despite (or sometimes because of) their best intentions. We're all just numbers on a spreadsheet.
Nobody expects morale to be great after layoffs. Do what you can, if you can, and try to compartmentalize and focus on what you're good at. Start looking for other work in the meantime, but don't count on being able to find another job, because many companies are folding in this economy and there's still a glut of programmers.
This isn't your fault. Companies exist to make money, and you're just another disposable cog in the wheel. Management exists to serve the owners/shareholders, not you, so your choices are really either to become more flexible (look for other jobs and careers, knowing that some will do better than others) or to become indispensable (either be exceptionally good at your job, or set up systems that only you can maintain).
Anxiety won't do you much good here because very little of it is actually under your control anyway. Just breathe; it's not up to you. Ultimately it doesn't really matter how hard you work and how great your code (or whatever) is; if your team isn't a good fit or your managers didn't put in the right reports or you didn't impress the right high-level person... you're disposable. And frankly, mostly invisible. It's unlikely anybody spends too much time thinking about your contributions to the company anyway, so don't spend too much time thinking about the company either. Most of us aren't special. That's okay though.
Don't let work define you! Develop other hobbies, enforce a strict 9-5 schedule for yourself and don't work late. Say "no" to things that break your work-life balance and find other ways to accrue happiness.
Especially in a startup atmosphere, it's basically gambling. You win some, you lose some. Just don't bet your whole life on it.