In California, employment is presumed to be at-will. See Cal. Lab.Code, § 2922. If you're employed at-will, absent unusual circumstances your employment can be terminated at any time, and you thus have no guarantee or promise of future employment. Also, an employer's economic condition is not fixed - its financial position can change, sometimes very quickly, and statements made in good faith may not be applicable even a couple of months later.
That doesn't mean that if you work for more than a month you're not at-will, or if the employer expresses that he hopes you will work there for a long time you're not at-will. It means that if your contractually promised term of employment is a month or more you cannot be terminated during that specified term absent good cause.Quoting California Labor Code, Sec. 2922.
There's authority that could support a potential promissory estoppel claim in the event that you quit a job in order to take the new employment and weren't offered the a good faith opportunity to perform his duties to the satisfaction of the new employer, even if the new work will be at-will. See, e.g., Sheppard v. Morgan Keegan & Co. (1990) 218 Cal.App.3d 61; Toscano v. Greene Music (2004) 124 Cal.App.4th 685. However, you did not quit a job so that theory cannot help you. You also worked two months at the new job, in contrast to those cases in which offers were withdrawn prior to the start date.
You can consult an employment lawyer with the details of your situation, but so far I'm not seeing either a basis to claim a right to continued employment or, in light of your prior unemployment and at-will employment with the new job, recoverable damages.

