I wouldn't use a screwdriver and hammer, as that's very likely to leave permanent scratch marks and other indentations, which will end up harboring infections later on.
I initially thought mine was stuck on as well the first time I used a bucket instead of a carboy. What I find works well for removing the lids that seem tighter than normal is to very carefully pry in just one spot using my fingers with all my force. I will put my left hand on the side of the bucket, and the right tightly gripping under the rim, and push/pull as hard as I can. That is usually enough to get it started. Once I'm able to get the lid moving just a little, it's just a matter of working at it for a bit to get it off.