(Well, let's assume what your log says isn't crazy, so you're on an older version. I guess that's all I really need to know!)

wget http://us.archive.ubuntu.com/ubuntu/...2.0-1_i386.deb
wget http://us.archive.ubuntu.com/ubuntu/....0-1_amd64.deb
if you're on 64 bit.

I'm on 32 bit, so:
ray@phoenix:/tmp$ wget http://us.archive.ubuntu.com/ubuntu/pool/universe/libw/libwebcam/libwebcam0_0.2.0-1_i386.deb
--2013-02-24 18:16:27--  http://us.archive.ubuntu.com/ubuntu/pool/universe/libw/libwebcam/libwebcam0_0.2.0-1_i386.deb
Resolving us.archive.ubuntu.com (us.archive.ubuntu.com)...,,
Connecting to us.archive.ubuntu.com (us.archive.ubuntu.com)||:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 23884 (23K) [application/x-debian-package]
Saving to: `libwebcam0_0.2.0-1_i386.deb'

100%[==========================================================================================================================================>] 23,884      --.-K/s   in 0.1s    

2013-02-24 18:16:28 (161 KB/s) - `libwebcam0_0.2.0-1_i386.deb' saved [23884/23884]

ray@phoenix:/tmp$ sudo dpkg -i libwebcam0_0.2.0-1_i386.deb 
[sudo] password for ray: 
Selecting previously unselected package libwebcam0.
(Reading database ... 184568 files and directories currently installed.)
Unpacking libwebcam0 (from libwebcam0_0.2.0-1_i386.deb) ...
Setting up libwebcam0 (0.2.0-1) ...
Processing triggers for libc-bin ...
ldconfig deferred processing now taking place
but after playing around, I decide the old version isn't fixing the problem, so:

ray@phoenix:/tmp$ sudo apt-get upgrade
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following packages have been kept back:
  linux-headers-generic linux-image-generic
The following packages will be upgraded:
1 upgraded, 0 newly installed, 0 to remove and 2 not upgraded.
Need to get 26.0 kB of archives.
After this operation, 18.4 kB disk space will be freed.
Do you want to continue [Y/n]?
and then I answer 'y', etc.