You should immediately consult with a lawyer who is experienced in condemnation/eminent domain matters.
The city cannot force you to sign the easement. However, the city can commence an eminent domain proceeding against you, through which it is possible for the city to take some of your property outright or obtain an easement. In eminent domain cases, the court is required to determine the amount of "just compensation" for any taking of property. However, one of the things that the court is required to consider is whether the taking if part of a larger project that also will confer a benefit on the property. If there are benefits conferred on the property, the value of those benefits must be offset and against the value of the property taken. Theoretically, the net result could conceivably be that you would not receive any compensation, but that would be an extremely unusual outcome.
The City should have the right to exercise eminent domain to acquire the easement using condemnation. Where the government has a valid public purpose, and has properly exercised its eminent domain power, the only issue left is to determine the amount of "just compensation" which will make the property owner whole. Your case involves a taking of a part of your property, so the just compensation must include not only the value of the portion of the property taken, but must also consider any impact to your remaining property. The amount of damages can be significant in certain cases, and will ultimately depend upon the degree of interference that the easement creates upon your remaining property.
Since you have not been offered any compensation, you should consult with an experienced eminent domain attorney in your State to determine the extent of your rights. Good luck!
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for advice regarding your individual situation.
No, you do not have to grant any easement without being compensated, and yes, if the City is forced to they can condemn the property for use as a street and/or sidewalk but in that case they must compensate you. This is a difficult negotiation to handle on your own because the government makes these deals every day but the average property owner will only deal with this once in their lifetime. You should hire an attorney.
I only practice in Washington State and may not practice in your area. This answer is a brief hopefully helpful tip to you which is correct to the best of my knowledge and is meant as a starting point for you to conduct further investigation. However, it is made without knowing the factual details of your case or doing any legal research and so may be in error as to either the facts or law. I am not your attorney and I am not giving a legal opinion by this answer.