If you are using TurboTax Desktop, make sure your program is updated. There were some HSA issues that the IRS did not resolve until fairly recently.
You are correct that your wife's Medicare coverage prevents her from being an individual eligible to contribute to an HSA but it has no effect on your eligibility for you to contribute to your HSA (an HSA has only one account holder).
The main reason you might get an 'overcontributed' error for your HSA is that TurboTax picked up your HSA contributions from your W-2, and you also entered them again in the HSA section.
If this is not the case, make sure you indicated 'Family Plan' for your HDHP coverage.
Click this link for more detailed info on HSA Overcontribution.
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