Can employer make a written offer for long term employment and then let me go after only 2 months without cause?

The answer to this question depends on quite a few variables.  First, was this written offer accepted and did it form the basis of a valid employment contract?  If not, then the employment may be considered "at will" which means that the employment relationship can be ended by either party at any time.  If there was a valid employment contract in place, you will want to pay attention to the "cause" definition included therein to ensure that the employer did not in fact have cause to terminate the agreement.