Yes, you can speak with the assistant d.a. and settle your case without an attorney. However, before doing so you should realize several things. The d.a.'s office has no obligation to "cut you a deal". They have no reason to let you know the problems they may have with the case and unless you are a lawyer, you probably do not realize how to look for the problems the state may have in the case.
An offer from the d.a.'s office should not change just because you hire an attorney. It doesn't get worse or better. The offer should change only when an attorney looks into all possible issues that may arise for the state. That could include in a DUI the basis for the stop. In a drug case, looking at the search warrant. In all cases, any statements made by you to the police and whether they are admissable. After spending time going through these and many other issues an experienced attorney can bring these matters before the district attorney and this may sway the district attorney in making his offer.
Being charged with and convicted of a criminal offense will impact you for the rest of your life. To ensure that all aspects of your case are covered, it is vital you seek the counsel of an experienced attorney. Yes, you could settle your case by yourself with the d.a. but be ready to plea to what you are charged and depending on that charge be prepared to spend time in jail. Criminal cases are complicated matters and handling them on your own can be overwhelming and ultimately have a devastating impact on your future.