If your aircraft is committed to an international flight and you are waiting on your permanent registration or you have not filed the registration paperwork yet, you can request priority handling. The FAA can fax you a 30-day Temporary Certificate of Registration which is good for operations outside of the United States. All documents must be in order and the aircraft must meet airworthiness requirements. Keep in mind this is for legitimately scheduled international operations as the FAA will check on you to verify you did make the flight. For more information click on the following link.
Normal FAA registration processing is currently at 5 ½ months. As noted by the OP, do not use this method to bypass the normal registration wait time and delay as there can be severe penalties for doing so.
If you recently sent registration documents through the normal channels, you will have to request an extension before the 90-day temporary authority expires. This can be done via the FAA webform here -