The theory that you need 300dpi to print is a bit misleading. 300dpi is good, but it doesn't mean it will look awful. Most estimates put human vision somewhere in the 250dpi area, with variation from person to person. To be safe, people quoted 300dpi as a figure.
The much vaunted Epson printers only used to print with 240dpi of detail, the remainder of the 5760 or whatever it is resolution is used to make smooth tones. (This information might have changed now I'm no longer current with newer Epson printers).
If you're going to pixel peep then yes the image will look less than impressive below as low as maybe 150dpi. But most people look at pictures for the image content rather than the pixel count or lack thereof.
The larger you print, the further away you naturally look at something, which means the resolution doesn't have to be that high.
In 2001 my rugby club won the local knockout cup at the time and the best camera around was the Nikon D1 which produced 2000x1312 pixel images. My champagne team shot at the end was enlarged to about 3m wide and it looks perfectly fine; if you can read the print on the shirt at 2000 pixels you can read the print on the shirt at 3m wide.
We won the cup again in 2004 and this time the cameras were D2Hs that shot 2464 x 1632 images. The club printed several promotional poster types from action images that were vertical crops of a horizontal frame, ie longest resolution was 1632 pixels. These were done to larger than life size, so about 2 and a bit metres. Same thing holds true, you could read the text on the shirt in the original image, so you can read the text in the posters.
Yes, okay, so you can't see the threads in the shirts. The question is, do you need to?
Your mileage will vary based on your subject as well. For something with lots of intricate detail then you will need a little more than you would if your subject was less detailed. So for example you would want closer to the 300dpi figure if you had a group shot of 100 people, for example. An evening silhouette you could get away with far, far less.
The quality of your 2000x1200 pixels also makes a huge difference; if they're good quality pixels and your image is sharp then you can enlarge a lot. If your 6000x4000 pixel image is out of focus and overexposed then it will look awful at 6x4 nevermind larger.
So don't be stuck on the 300dpi figure.
