Walleye1 is right about two 1,500 watt elements on a 110v feed. It is going to draw over 27 amps just for the heating elements and most 110v household circuits are only 15amp rated (some are 20). So unless you are powering it from a 30am RV type outlet with appropriate wiring, you will trip the breaker constantly. 220v is the way to go with that much wattage, but you cannot just put a 1,500 watt element (like the brinkman elements) on a 220v feed. If you go 220v, make sure the elements are rated for that voltage level.
Another option if you have 1,500 watt 110v elements, is to feed the smoker from a 220v line, but split the 220v into two 110v circuits inside the cabinet. You take L1 to neutral for one circuit, and L2 to neutral for the other (Normally for 220v it's L1 to L2 and the neutral is not used). You would need two SSR's to wire it this way, but you can trigger them from a single PID with no problems.
Either way, with 3,000 watts of load you are going to end up on either a dedicated 30amp RV type circuit or a dedicated 220v circuit.