The print queue pauses, and a dialog box says the user is not a member of the "Printer Operator Group." If that user doesn't know an admin user name & password, they're out of luck.
Apple.com has a solution, but the website says it only works for 10.5, not Snow Leopard (10.6).
Fortunately, Palindrome.com (Paul Rauschelbach) has found that it works for 10.6 as well. I'll let him explain...