During construction I ran 14/2 NM cable from a junction box to all of my cabinet boxes. Will I have any issues running the low voltage on the 14/2

No, you should not have any problems running your 12-volt power supply output on your 14 gauge cable. We would not recommend soldering such heavy gauge wire directly to the tape lighting itself, but you can make simple wire splices to smaller gauge wire, or to our SureLock family of connectors for your tape light connections. Be sure to properly support your wiring so it does not create any strain on your tape light connections. For further assistance, please contact our support staff at support@armacostlighting.com