Happened to my launch-week iPhone 6 Plus. Apple employees at the store were aware that phones had this issue but acted like it wasn't a problem they could treat. They treated it as a "bad screen" problem by replacing screens. After a couple of screen replacements the issue didn't go away.

Ultimately, I had to pay $329.00 for a refurbished phone after they swapped out a few screens which didn't make the problem go away.

There is a class action lawsuit forming: http://mccunewright.com/iphone-6-touchscreen-defect/