From previous threads on the Dis, it sounds like fraud can cause problems, depending on the bank involved. Some banks are great and will credit the disputed amount while under investigation, others will say "too bad so sad" and leave you hanging. Sometimes overdraft fees and bounced check fees occur before the fraud is discovered as well, and not everyone has luck getting those waived.
Before switching to using debit as your primary source of paying for things, I would go to you bank and sit down with a manager, and find out exactly what would happen if there is fraud. If it sounds like they won't help you, you can either figure out another way to pay for purchases or switch to a bank with better fraud protection on debit transactions.