I've done this - it's not a fix but it makes the steering less over-sensitive. There's still lag though, which is by design and it SUCKS!
Locate your player save folder, found normally in [Your User Folder]\Documents\Criterion Games\Need For Speed(TM) Most Wanted.
From there, open folder "Save", then the folder with a long number.
Open file "controls.NFS13Save" in notepad.
Find the lines that correspond to your left and right steering configs with your desired controller. It'll look like this:
[Config_Xbox 360 Controller for Windows]
STEERLEFT=0,X_AXIS (LS),0.00,-1.30
STEERRIGHT=0,X_AXIS (LS),0.00,1.30
Notice that I've changed the final range numbers from -1.00 in the first line and 1.00 in the second to -1.30 and 1.30 respectively.
This cuts down a lot on over-sensitivity and made the game at least minimally playable for me. The numbers themselves can be set to anything you like, but the larger numbers you choose, the less maximum steering range you'll have. I found +- 1.3 to be the best setting for me. I still HATE the steering lag that is built into the game and for my $53 I want it FIXED!! but I hope this helps in the meantime.