Unfortunately, you probably do not have a claim against your employer. If your termination was unrelated to your membership in a protected category (such as age, race, sex, disability, etc...) or some other violation of the law (such as whistleblowing) and you have no employment contract and are not in a union, there's probably no claim.
Not the best way to go about terminating your employment and I certainly understand how it could be embarrassing, but you were most likely an "at will" employee. This means you could be terminated for any reason, or no reason at all, at any time so long as it isn't based on discriminatory reasons (i.e. because of race, sex, national origin or another protected classification), or your having engaged in a protected activity, or in violation of the terms of a contract or collective bargaining agreement, Therefore, you could be terminated for "burning leads" and you won't have any recourse. Sorry...
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While not the best practice, firing someone over the intercomm is not illegal. Moreover, employers have a qualified privileged to make statements regarding their employees that might otherwise be defamatory.
Moreover, statements of opinions are not actionable. Generally, in most states to overcome the qualified privilege you would need to prove that your employer made false statements about you with actual malice.
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As an at-will employee, the firing does not sound unlawful. So, the remaining question is whether announcing the fact and the true reason you were fired over the intercom for your coworkers to hear unlawful?
If you were truly "burning leads" - whatever that means - then the announcement of this true fact over the intercom is not illegal. It is not within the "zone of privacy" to be protected from public disclosure, unlike for example your medical information, or other personal and private details.
If the announcement that you were "burning leads" is a lie, then you could theoretically have same claim for slander or intentional infliction of emotional distress. But, more practically speaking, whether these are weak claims not worth pursuing is something you might discuss with an employment lawyer. In fact, an emotional distress claim here is probably preempted by the workers' compensation law.
Overall, this does not sound like a claim with pursuing based on the limited information available.
I'm sorry you experienced this humiliation. I hope this information is helpful to you. Good luck!
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There would not typically be any legal claim on the basis of the facts you have described. I am sorry.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents.