This answer is outdated. See my other answer for newer information.
I solved this by installing KX Studio. The instructions can be found here: http://kxstudio.sourceforge.net/Documentation
These are the steps I used. (They are directly from the KX Studio documentation.) In my case it was required to install the low latency kernel. I tried the generic kernel first and that did not do the trick. Once I installed KX Studio and the kxstudio-kernel-lowlatency, my audio interface "just worked."
Step 1 - Enable the repositories
Open up the 'Software Sources' (usually in the System menu), and on the 3rd party separator, add this code:
Alternatively, you can run this command, which has the same effect:
sudo add-apt-repository ppa:kxstudio-team/kxstudio
Next, reload the sources (method depends on the current application), and install the package 'kxstudio-repos'. Then reload the sources again.
You can do the same thing in the command-line with:
sudo apt-get update
sudo apt-get install kxstudio-repos
sudo apt-get update
NOTE: If you're running 12.04, it's recommended to also install 'kxstudio-repos-kde49' which will update KDE4 to the stable 4.9.5 version.
Step 2 - Update the system
Once you've got the repositories set-up, it's time to upgrade the system (ie, update the software, not upgrade to a newer Ubuntu release!).
Simply use whatever tool your Desktop Environment provides (Ubuntu Software Center, Synaptic, Update Manager, KPackageKit, Muon, etc).
If you want to use the command-line, or if you just got too many dependency conflicts (can happen if you enabled many PPAs before upgrading to KXStudio), the command is:
sudo apt-get dist-upgrade
Even though it says 'dist-upgrade', it will not update the Ubuntu version. In this case, 'dist' means something like "resolve conflicts, even if some stuff gets removed".
This step will take some time. Some minor questions may appear while the upgrade takes place.
Step 3 - Install the KXStudio Desktop
After the upgrade, it's time to install the main KXStudio packages.
Just like you did to install the 'kxstudio-repos' package, now install:
For KDE4 -> 'kxstudio-desktop-kde4'
For XFCE -> 'kxstudio-desktop-xfce'
For other systems install 'kxstudio-desktop-base' and the ubuntu related package, like 'lubuntu-desktop' for LXDE
Step 4 - Install the Multimedia Software
This step if almost optional. Here we install the basic software for Audio, Graphics and Video.
Just like before, it's time to install some new meta-packages. They are available as listed here (following a tree view of dependencies):
Install the meta-packages you want just like before (ie, search for the package and click to install, or use in command-line: sudo apt-get install )
See Documentation:Ubuntu:Meta-Packages for a description of these meta-packages.
Note - meta-all recommends restricted extras, and audio recommends audio-plugins.
Step 5 - Install a Kernel
This step was required in my case. And the generic kernel was not enough. I had to install kxstudio-kernel-lowlatency.
Installing a kernel in KXStudio couldn't be easier - just install one of these packages:
kxstudio-kernel-generic-pae (32bit only)
kxstudio-kernel-lowlatency-pae (32bit only)
kxstudio-kernel-realtime (10.04 or 12.04)
kxstudio-kernel-realtime-pae (10.04 or 12.04, 32bit only)
The realtime kernels are only available for 10.04 and 12.04.
Ubuntu 10.04 uses a 2.6.33 RT kernel and 12.04 uses a 3.2.0 one.
Step 6 - Reboot and update settings
After all this, it's time to reboot.
The next time you login, you'll see the KXStudio Welcome Screen to help you update your settings (and maybe the theme too).
You should also run 'cadence' and change your JACK settings to your preference.
Finally, just re-login again after updating the settings.
Step 7 - Enjoy!
Of course, now it's time to enjoy!