Umm, it is your responsibility. You were the driver. It is your job to make sure you have all your paperwork and a safe and properly equipped vehicle before you drive it (even if obtaining the documentation is your employers). I can't believe anybody claiming to be a "lead driver" doesn't know this and doesn't know he needs a medical card.
If you can't pass the medical, you have no business being a commercial driver. They're almost a sham to get. What do you mean you can't get one?

