Yes, money talks, though all it ever said to me was "goodbye". :-)
Seriously, some banks are better than others at giving credit cards and overdraft facilities to foreigners. Most don't, however some (pre-credit crunch) certainly used to. A Karta Pobytu etc would be a minimum requirement. Even then, a lot depends on luck - a refusal is the most likely response.
I still think the OP should try in their home country - they are 99.9% more likely to be successful there.