I appreciate the additional information.
1. There is a difference between a contract for employment and a NDA. Typical employment contracts set forth details of work to be done, hours, severeance, pay, bonuses, and duration. NDA's concern and restrict your employment opportunities after you terminate your position.
2. I'll ceretainly accept your description as being litigious, because they are also cheap. NDA's are appropriate for two classes of employees: (1) engineers and inventors, (people who develop products and have access to secret information, and (2) high profile execs, (normally sales types that take accounts with them or have the ability to). Here, it is clear that the company has gone out and bought some generic NDA, probably off the internet. It is not appropriate for your job description. As such, it may or may not have direct impact on you. The only way to know for sure would be to set down with a local attorney. There is no substitute for that.
3. In Colorado, there are very limited circumstances in which a non-disclosure and non-compete covenant can be enforceable. Only you can tell if it is applicable in your situation, and again, this is something you could specifically discuss with a local attorney. Here is the link to the law:
4. The question as to whether they can fire you is closely tied to the statute above. Either way, yes, they can terminate you without a seperate contract between you and the company. However, the issue of damages or unemployment is still not resolved. Without the contract for employment, you are an employee "at will" and subject to termination at any time, but it might still be illegal to fire you for refusing to sign the agreement.
Your situation is complicated, and it cannot be completely resolved here. I seldom recommend this, but in your case, it would be a good idea to pay for an hour or so of an attorney's time. Good ones charge for their time. These types of consultations are affordable, usually a flat fee, but this would be money well spent.
I do hope this helps.
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