Safeguarding Individual Privacy Against Government Invasion Act of 2014 - Amends the Privacy Act of 1974 to specify that the liability of the United States in a civil action brought by an individual adversely affected by a federal agency's intentional or willful failure to maintain accurate records concerning the individual is provable damages, including damages that are not pecuniary damages, sustained by the individual as a result of the refusal or failure, or $1,000, whichever is greater. (Currently, the United States is liable for actual damages, a term that is interpreted to be limited to economic harm or pecuniary damages, which excludes damages for mental or emotional distress.)