No such animal as a "safe job", even the postal service is eliminating people.
As you evaluate a prospective employer-- consider their business model and markets they serve. Are they expanding? Does the senior leadership have experience and stability?
Relative to Yahoo/Twitter engineers-- some of those guys are getting fat severance packages and plan to chill on the beach for the next 18 months. Don't worry about them. Move when the right opportunity lines up for you.