There are many facts that need to be hashed out in order for an attorney to be able to properly answer your question. Most importantly, what is the charge in the case? If it is a domestic violence dispute, the fact that a victim is not willing to testify does not preclude a prosecutor from pursuing a criminal action against you. In fact, many times the alleged victims in these types of cases are unwilling to testify, and yet defendants are still are charged and taken to trial for domestic violence.
You state that it was a simple argument–where there criminal threats made? Did the other person in the argument fear for their safety because of the argument? Again, once the police are aware of such facts, the alleged victim need not consent for the prosecutor to go forward.
If you have a warrant out for you, then that likely means you are being charged with a crime, and you should hire an attorney right away. Once an attorney is able to learn all the facts, then they can work to get your case dismissed if necessary.