Module for getting what is visible from user's webcam
I don't think there is exactly what you want at the moment, but the following module might help you on your way:

Webcam field - This is still in development


  Webcam field provides dynamically updating webcam image fields. This
  module is compatible with Colorbox.


Videochat - Has no recommended release, although seems to have a full 3.6 version


  The Video Chat module adds a fully hosted free video chat to a Drupal
  website. The chat application and video hosting are courtesy of
  Camamba and ad-supported. We hope it provides an alternative to all
  the payware chat modules out there.


Media: Webcam - This is in beta


  This project (still under active development) will add a Webcam
  capture tool for video and images to FileField. Video requires a Red5
  or Flash Media server to also be available; documentation for this
  coming soon enough.


Video conference - This requires some further set up of server components, but if you want live video streaming I should imagine you're aware that you will most likely need a RTMP protocol set up.


  VideoWhisper Video Conference is a modern web based multiple way video
  chat and real time file sharing tool. It can be used stand alone or
  integrated as extra feature to existing sites. Internet based video
  conference software is great for bringing physically distant people
  together in meetings, trainings, conferences, live events, recruiting,
  consultations, coaching and of course casual community chat.


Paid solution

AVChat

This comes at a price of $285 plus $49 for the Drupal module