CanI go to jail for voicemail that involved threatening words that was caused from a mutual argument?

You have to make a decision as to whether or not you feel confident that the District Attorney will be able to prove its case against you or not. Like the previous answer explained, the issue is not whether the argument was mutual but whether the words used constitute a threat and were intended to harass and annoy the complaining witness. If they were and you do not have a valid defense, you could be convicted. You can however argue that the argument was mutual and thus the threat was provoked and therefore you did not intend to harass the other party or he/she was in fact not threatened by it and knew it was just words. I am not sure if there is any offer on the table to resolve the matter but you certainly should have your attorney talk to the DA to see if there are possible alternatives. If you are charged with aggravated harassment which you probably are, a conviction is criminal and result in jail time or probation and even if you get neither it could affect future life endeavors.

As you are now aware, threatening is considered a crime, and you can be prosecuted for it regardless of whether or not the alleged "threat" resulted from a mutual agreement.  If you were arrested after you went down to the precinct to "discuss" the matter, chances are that you said or signed something that can be considered incriminating.  Depending on the degree of the charge, it is certainly possible that, if convicted, you could be sentenced to a period of incarceration.  However, from procedural perspective, it is not clear that just because the prosecution said that they are "ready" to go to trial that the matter actually will go to trial.  Nevertheless, given the potential consequences of a conviction I strongly suggest you consult with and/or retain an experienced criminal defense attorney in the interest of obtaining the best possible resolution of this matter.