Technical Description of OBD-II Trouble Code
The circuit for supplying power to the sensor is open
What does that signify?
This is a generic diagnostic trouble code (DTC) that is applicable to many OBD-II vehicles (1996-newer). This includes vehicles from various manufacturers such as Buick, Chevrolet, Chrysler, Fiat, Ford, GMC, and Mercedes-Benz, among others. Although it is a generic code, the specific repair steps may vary depending on the year, make, model, and powertrain configuration of the vehicle.
When a vehicle equipped with OBD-II has stored a code P06B3, it means that the powertrain control module (PCM) has failed to detect the power supply voltage for a specific sensor or group of sensors. Depending on the manufacturer, the sensor(s) in question may be related to the exhaust gas recirculation system, the heated exhaust oxygen sensor system, the automatic transmission, or the transfer case (only for four-wheel drive or all-wheel drive vehicles). The affected sensor circuit is designated as B (A & B can also be interchanged).
Most OBD-II sensors are activated by a voltage signal provided by the PCM or one of the other on-board controllers. The applied voltage (often referred to as reference voltage) can range from very low voltage (typically measured in millivolts) to the full battery voltage. The most common sensor voltage signal is 5 volts, followed closely by battery voltage. It is important to determine which sensor is related to this code, and reliable vehicle information can provide this information.
If the PCM (or any of the other on-board controllers) fails to detect voltage on the power supply circuit designated as B, the code P06B3 may be stored and the service engine soon/malfunction indicator lamp (SES/MIL) may illuminate. Illumination of the SES/MIL may require multiple ignition cycles with a failure.
A typical opened up PCM powertrain control module:

What is the severity of this DTC?
I would classify this code as severe. The inclusion of a wide range of sensors makes it difficult, if not impossible, to precisely determine the severity of the symptoms caused by the condition that led to the storage of the P06B3 code.
What are some of the symptoms of the code?
Symptoms of a P06B3 trouble code may include:
What are some of the common causes of the code?
Possible causes for this code may include:
What are some P06B3 troubleshooting steps?
Prior to attempting a diagnosis for the stored P06B3 code, diagnose and repair any other sensor-related codes.
To accurately diagnose a code P06B3, you will need a diagnostic scanner, a digital volt/ohmmeter (DVOM), and a reliable source of vehicle information.
Without the means to reprogram controllers, reaching an accurate diagnostic conclusion for the stored P06B3 code will be challenging at best. It may be helpful to search for technical service bulletins (TSB) that match the stored code, vehicle (year, make, model, and engine), and exhibited symptoms. This information can be found in your vehicle information source. If you find the appropriate TSB, it can provide valuable diagnostic information.
Connect the scanner to the vehicle diagnostic port and retrieve all stored codes and relevant freeze frame data. After recording this information (in case the code is intermittent), clear the codes and test drive the vehicle. One of two things will happen: the code will reappear or the PCM will enter readiness mode.
If the PCM enters readiness mode (indicating an intermittent code), the code may be more difficult to diagnose. The condition that caused the P06B3 code to be stored may need to worsen before an accurate diagnostic conclusion can be reached. However, if the code reappears, continue with your diagnosis.
Obtain connector face views, connector pinout charts, component locators, wiring diagrams, and diagnostic flow charts (specific to the code and vehicle in question) using your source of vehicle information.
Visually inspect all related wiring and connectors. Repair or replace any wiring that has been cut, burned, or damaged. It may also be necessary to check chassis and engine grounds and make any necessary repairs before proceeding. Use your vehicle information source to obtain ground junction locations for related circuits.
If no other codes are stored and the P06B3 code continues to reset, use the DVOM to test controller power supply fuses and relays. Replace any blown fuses, relays, and fusible links as needed. Always test fuses with the circuit loaded to avoid misdiagnosis.
If all controller power (input) and ground circuits are intact and there is no sensor power (output) supply voltage being output from the PCM (or other controller), a defective controller or controller programming error may be suspected. Keep in mind that replacing a controller will require reprogramming. Aftermarket sources may offer reprogrammed controllers for some applications, while other vehicles/controllers may require on-board reprogramming that can only be done through a dealership or other qualified source.
Visually inspect system controllers for signs of water, heat, or collision damage. Suspect that any controller showing signs of damage is defective.