Personally, I'd be far more concerned with ID fraud than attacks on the encryption scheme. How do they determine who's using the 'hardened laptop'?

Maybe they do the same simple thing that we do at the good old fashioned polling place where I work each election in King County, Washington. Before we allow them to mark a paper ballot with a pen (or step up to the electronic machine, if that's their preference) we ask to see their government-issued ID. Your state election laws may vary.