The answer from spyder is NOT correct. The flasher for the 2002 Vue is integrated with the hazard switch. If there is a problem with the hazard switch, it usually takes out the turn signals also. The switch/flasher unit is relatively easy to replace (I replaced mine in about 15 minutes using only a 7mm nut driver). Instructions on how to get at the hazard switch can be found at "http://wiki.answers.com/Q/How_do_you_remove_a_Saturn_Vue_dashboard". This walks you through how to remove the panel in front of the radio which just happens to hold the hazard switch/flasher unit. The switch/flasher unit clips in to the back of the panel. You just have to be careful not to break the locking clips when you remove the old switch.
Just got done taking the console out of my vue. Had to order the new flasher relay. My symptoms were that I lost my daytime driving lights first. Then after you turn on the turn signals a clicking sound would continue after the turn signal had clicked to the off position. It was making me nuts. Taking the console out wasn't that bad but you want to make sure the plactic components are not cold or parts could snap.
This is your control module beginning to fail. That's how mine started going out. My turn signals would mysteriously fail and then mysteriously start working again. Over time, more things start working improperly. My car doors began to try to lock every 30 seconds, my engine fan started not working properly. The key would have been to force the dealership to find the failure and replace the module for free under warranty but usually by the time you figure out what's wrong or can handle waiting for the car to fail for the techs at Saturn.....your warranty is probably long gone.