Miners can vary at least these things when searching for hashes:
- A 32-bit nonce
- Which transactions are included in the block.
Is it ever possible for a currency using the Bitcoin protocol to get 'stuck'? That is, can all combinations of parameters that miners are allowed to tweak not result in a hash that conforms to the difficulty?
One scenario using those parameters I listed could be an ASIC miner working on a brand new network. The difficulty should rise extremely quickly, but there would be very few transactions for him to work with.