Wow, not to sound like a douche or an elitist but, it seems none of you know what you're actually talking about and have done any real extensive research into the subject matter. You can't see/feel 2-3 ms it's not possible. There are so many discussions and points about this on MIOM and facebook, get wrecked.
Anyway, I'll just explain most of the misunderstandings and the lies you've been fed. Response time has very little to do with the lag that gamers speak of. Response time is the time it takes for the pixels to turn from black to white to gray. So this only really has anything to do with how fast the pixels change which in turn only has anything to do with the effect of ghosting. Ghosting is when you see tearing or blurring of the pixels due to them having to process changing to a different color due to motion. So it's kind of like motion blur.
This is not the lag everyone is talking about. It's input lag that affects gamers heavily. When you input something on to your console, it has to send that signal to your TV. This has to do with signaling/modulation (digital vs analog situation). First off, analog has either no or very little lag due to the fact that it does not have to process that it received a signal to output it while digital, it has to go through and process out each pixel/image and know that it received a change in the image due to an input being sent. That input has to be acknowledged and processed and then outputted.
Input lag is not advertised due to it being only important to only such a small consumer base so they don't ever advertise it. It's also different at different refresh rates and different motion smoothing processing bs that they use nowadays with the LED LCD TVs. Input lag on LCDs occurs for multiple reasons, the native input lag a monitor/tv has (all LCDs have input lag due to processing the image/input), whether the image is outputted at native resolution or a different resolution, and what signal is being used to output the image.
To put in perspective to Smash, the reason why we use CRTs is because there is virtually no input lag. The reason why lag is bad for Smash and why people complain about is due to many reasons.
1. LCD monitors have at best about 10-15ms input lag, a frame is 16.67ms. Inputs will be processed less than a frame late. This is not an issue whatsoever but, that's how much the best monitors have. An average LCD HDTV/Plasma has anywhere from 20ms-100+ms natively. That's more than a frame so imainge your inputs coming out/being recognized 2+ frames late. You'll be timing things off, and it's not like spamming is an option in melee, especially with strict timing windows for general tech. NOTE: Native input lag is not the actual input lag (it's wayyyy more) you would receive in Smash.
2. Smash is not natively an HD game, meaning it's outputted natively at 640x480 while an LCD TV/MONITOR on average outputs natively at 1920x1080. Upscaling and downscaling (or any non native res) will cause more processing to occur. So imagine, you can end up getting about 50+ms of input lag due to all the processing the TV is doing to display the image.
3. Gamecube/Wii uses analog signaling on default. 480i is an analog signal/resolution and that's the default that these consoles have. While they do have component cables, they are not cheap or easy to find anymore, so that analog to digital processing also adds more input lag.
So if you're playing Smash on an LCD TV/Monitor via composite, you'll be receiving noticable input lag due to image processing, signal conversion, and upscaling. Having to try and execute technical things, even just SHFFLing at the fastest possible rate, you'll be having to press frames earlier than you're supposed to which, technically is not possible because it takes time for the TV to process that input anyway. So no matter what LCDs have lag. Remember, response time has very little to do with this.
Although, there are ways around all this with hardware accelerators as mentioned above, Avermedia LGPs which allow very fast signal conversion from analog to digital. People from the Smash community have done extensive testing and have come to the conclusion that you can get lower than 1 frame of lag which is said to be impossible to actually noticce due to the human reaction time only being so fast.