Cedarjet, what problems are you expecting? That you will need your passport while the visa is being processed?
I would suggest making a copy of your passport and carry it with you while the visa is being processed. This way you would be able to explain your "unindentifiable" status. Bring your driver's license too. Sometimes it may be used as a photo ID.
Yes, apparently the China Embassy in Singapore requires 4 working days to process the visa. You can, however pay an extra S$50/S$35 for a same day/next day service. The Chinese Embassy is at Tanglin Road. For more info,
http://www.chinaembassy.org.sg/eng/lsqw/default.htm
Hope this helps.