In order to prevail on a DUI prosecution, the State must prove that you were substantially incapable of operating a motor vehicle t the time you were driving a car. Before they win, you have the right to challenge whether or not the officer had probable cause to arrest you for DUI. It is likely that the officer used your failures on this particular test in formulating probable cause. Thus, you can challenge the result due to your balance challenge.
All that said, you need to consult with an experienced criminal defense attorney to discuss the possibilities. Some prosecutors say that if you challenge your arrest, they will withdraw potential plea bargain offers if they prevail against the challenge. Because that may cut against your ultimate goals, a good lawyer is a must!
Best of luck.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.