Adobe Illustrator file exporting and pixel previewing blurry - HELP!

Lukas gave some good suggestions, anti-aliasing options, Photoshop resampling.

I would add to keep your design well beyond the limits of the pixels you will be using in the final result, check the font Size (don't make it too small) and the font Style (light maybe too thin).

Ton gives you a good answer, you are cominhg to the limits of what is possible to reproduce considering the number of pixels you use.

When exporting to a given number of pixels text especially either must follow the pixel grid, which means rounding up or down in number of pixels causing small text to appear irregular, or text needs to be antialiased (you can not maka half  a pixel white but you can make the colour of the pixel half way between the background and white) which gives a slightly blurred appearance. Text can be set to follow one of several alogrithims to get the best possible result (which you must determine what is suitable) 

From the Character panel show advanced options, next to where you choose language you may choose from: None, Sharp, Crisp or Strong as method for antialiasing, note this can only be done at object level the menu is unavailabe if you have characters selected. 

Also see antialiasing setting on the export which allows none, object or type optimised.

Photoshop has more options for optimising pixels, some users will prefer to export from illustrator with a larger number of pixels and downsample to the correct pixel sixe in Photohop.

I am afraid that you run into the limitations of what can be represented with that small amount of pixels (already visible when you check with Pixel Preview). Exporting at 2X and scaling it down at the web page will improve it.