Hi ecwman,
Does the issue persist with another headset?
If it doesn't, there may be an issue with the headset.
If it does, there may be debris in the iPhone headphone jack. Try connecting and disconnecting the headphones a few times.
You can request repair or replacement of the iPhone Stereo Headset online here:
https://selfsolve.apple.com/GetWarranty.do
Also, you can get the iPhone or headset replaced by making a reservation with a Genius or calling AppleCare.
http://www.apple.com/retail/geniusbar/
U.S. iPhone technical support: 1-800-MY-IPHONE (1-800-694-7466)
-Jason