Barry --
These men were concerned about unfairness of an extension of their term of service until April 16, 1862.
However, several weeks after this document was written, Congress decided to call all twelve-month men back into service. If a soldier didn't have an exemption from service and failed to report as required (thirty days from April 16, 1862), by law he became subject to conscription. That meant obligatory military service -- a conscript officer appearing at his gate to provide an escort to camp of instruction.