MichaelMeissner:
One alternative is to use an HDMI switcher. You can get these cables for $5-10 from Hong Kong merchants. Here is the cable sold by an Amazon reseller: http://www.amazon.com/SANOXY-Switch-Switcher-Blu-Ray-HD-DVD/dp/B0040G5KY6/ref=sr_1_2?ie=UTF8&qid=1345843556&sr=8-2&keywords=hdmi+switch+boxesI would imagine if you open the box, it should be fairly easy to have the arduino control the switcher by simulating the button press with an opto-isolator.
That's a very good suggestion! It should be cheaper and easier to wire into a switching hub like that one. The schematics probably aren't easily available, but it should be fairly simple to identify the trace connected to the switch.
However, I would be sure to measue the voltage outputed by the switch before connecting it to an Arduino. It appears to not have any dedicated power supply. So the voltage levels are likely whatever the manufacturer considered most convenient to get from the HDMI cables, and that could be something either higher or lower than the 5 VDC from an Arduino pin. At worst that means a bit additional level shifting circuitry, but it's something that should be detemined before connecting the Arduino.