can the da make a defendant go to trial?

No, a DA cannot make a defendant go to trial.  However, if the DA has not given you an offer the only way to avoid trial is to enter an "open" plea of  guilty or no contest to the charge or charges.  This means you would be exposed to the maximum sentence without any sort of cap on your punishment.  The DA would be free to ask for the maximum in that case.  You and your attorney would be able to ask for less, of course.  You should speak to your attorney about all of your options, even if the DA does not want to make an offer.