Paul can correct me if I'm wrong, but I just don't think the Teensy 3.0 has enough memory and/or CPU speed to handle display of HDMI on a non-HDMI screen. Now, if you step up to one of the embedded Linux boards (Rasberry Pi, Beagle Bone Black, pcDunio), or standalone Android devices (like the MK802 mini PC), these all have HDMI output, and graphics co-processors to help output HDMI. Perhaps they have enough horse power, to create a display from a HDMI input, perhaps they don't.
So lets step back, and look at what can be done.
While you might be able to create your display using a generic screen to do HDMI (or even composite video), it will likely take a lot of work to write something that acts like a TV in real time (i.e. 1920x1080x3 pixels 30 times a second for high defintiion). If you are up for the challenge, more power to you (and hopefully you will share your software when you get it done). You can reduce the processing requirements somewhat by using 320x240, which more matches the small screen), but it still may be a slog do it.
Instead, what a lot of people do is use somebody else's monitor. You could use the guts from video gamer glasses, such as:
http://www.adafruit.com/products/1452 which takes composite video (NTSC/PAL) and not HDMI.
You could search around for a small MP4 player with video input capabilities. In the past, I found a very few, but the last time I did a search, I couldn't find any that take video input. If you wanted larger screens, some DVD players have video input (such as my wife's 9" Sony). Some pocket video cameras have had video input in the past (I have a Wolverine unit that took composite video input, but it went out of production 2-3 years ago).
In terms of cheap displays, you can find displays for car backup monitors fairly cheaply ($20-40). These displays don't tend to take HDMI, instead they take the older composite video input (think back to NTSC/PAL with the yellow RCA jacks). Now, here the PI is perhaps better than the others, since it still has composite video output, while I think the others only have HDMI. Here is the cheapest 2.5" lcd that I've seen on ebay:
http://www.ebay.com/itm/Digital-Sli...t=Car_Audio_Video&hash=item4cf1cbe172&vxp=mtr.
Adafruit.com sells a bunch of small monitors that take NTSC/PAL that might work. I must caution you, I was wanting to create something like what you are striving for, and I bought one, and I had my wires mixed up, and fed the ground to the power circut and vice versa, and I created a $40 piece of slag. Here is a unit with a 1.5" screen:
http://www.adafruit.com/products/910. I keep meaning to get back to this. I have a larger MP4 player that I occasionally use as output for my steampunk camera.
Now, one place that I've bookmarked is Vizic technologies that offers smart displays that can be interfaced from microprocessors like the Teensy:
http://vizictechnologies.com/.
Another place I've bookmarked is New Haven Displays. They have a lot of different displays, but I'm not sure they would do what you want:
http://www.newhavendisplay.com/.
If you were thinking about doing custom displays for prototyping Android systems, you might look into Liquid ware:
http://www.liquidware.com/.
I've bookmarked this ebay site, which seems to have more different displays for Arduino/Due/etc.
http://stores.ebay.com/coldtears-el...30141016&_sid=680237586&_trksid=p4634.c0.m322.
Another display company I've bookmarked includes:
http://www.usmicroproducts.com/.
This company has small handheld monitors:
http://www.lcdtft.com, though compared to the car backup monitors, they are a little pricey.
I keep hoping when google glasses become more widespread, it will cause more variety in knock off competitors.
As I was writing this, I was wondering what the cheapest small HDMI display was. I saw this 3.5" monitor meant for videographers on ebay:
http://www.ebay.com/itm/3-5-inch-Co...pt=US_Viewfinders_Eyecups&hash=item4ac07dae33.
Adafruit has a 7" HDMI/IPS display, which you really don't want to wear on your eyeglasses:
http://www.adafruit.com/products/1033, and a cheaper NTSC/PAL 7" display:
http://www.adafruit.com/products/947
If you had an Arduino Uno (not Mega, and probably not Teensy 2.0/2.0++), there is the video experimenter shield from nootropic, that allows you to overlay monochrome text and block graphics over a video stream:
http://nootropicdesign.com/ve/