Unless you have an employment contract, they can ask you to sign and probably let you go if you don't. It does seem excessive, perhaps you can negotiate one that says lets say ten miles from your work location.
You may want to consult with a lawyer before you discuss with the boss.
Florida is an at-will employment state. This means that, unless you have an employment contract, you can quit your job at any time for any reason. Conversely, it also means that an employer can fire you at any time for any reason or for no reason at all. If the employer states a reason for termination, that reason cannot be discriminatory — it cannot be based on your age, sex, disability, race, national origin, or marital status. If you employer fires you for failure or refusal to sign a non-compete agreement, the employer’s action would certainly seem unfair, but would likely not be deemed discriminatory (unless there are a lot of other factors involved that you have omitted).
Non-compete agreements in Florida are generally enforceable so long as they are reasonable in terms of scope (geographic area and line of business) and duration (length of time). Additionally, there has to be a legitimate business interest (e.g. trade secrets; confidential business information) that is protected by the non-compete. Florida does NOT require, however, that an employee be given consideration (something valuable to induce you to sign the agreement) in exchange for signing a non-compete, other than continued employment, which courts have deemed to be sufficient.
I agree with my colleague that 60 miles seems excessive and may be something that can be negotiated to a more reasonable area that would accommodate the needs of both you and your employer. I recommend that you contact an attorney to read through the agreement and assist you in negotiating its terms.
This response does not create an attorney-client relationship and is not intended to provide legal advice for your specific situation
What is the consideration for you signing the non-compete clause? In order to be bound by this agreement they would have to give you something which you already do not have. The Funeral Home may say continued employment i.e. If you want to continue to work for us you must sign the agreement. However, your answer does not indicate this so am not going to assume that was mentioned.
Most courts will look to the reasonableness of the contract to determine if it is enforcable but it must be limited in scope and location. For instance if you were to get One Million dollars not to compete for 2 year and sixty miles that would seem to me very very reaosnable if you were to get One Hundred dollars that would be unreasonable.