Where does GPS interference such as that from Lightsquared come from?
I work in an industry affected by the LightSquared system and may be able to provide some insight. The issue at hand does fall into the area of being with the GPS receiver. The bands that LightSquared wants to use are near the GPS L1 wavelength. These bands are currently employed by systems that send command and control packets to satellite systems. However the LightSquared signals are orders of magnitude greater in strength. The RF filters on high precision (dual frequency) receivers were not designed to block that much power at the edges of their bands and this is where the interference comes from. So, an industry never expected an adjacent band to be used in this manner and thus opted to save money (and a significant amount in the early days of GPS) on their filter design. At this point with the hundreds of thousands of high precision receivers in the field it has gotten to the point that the easiest fix is for LightSquared to employ better filters on their end. Otherwise most military and survey grade receivers will have to replaced or fitted with new supplemental filters. 

Once I am at my desktop I will update with some graphics showing the power and frequency distribution of the applicable signals.

EDIT:

As promised here is the update. From the below image you can easily see the power envelope of the LightSquared LTE signal. (This image originally came from: Javad's website, who is a manufacturer of GNSS receivers) Also, on the graph are the frequency response plots of some fairly typical filters used in various types of GPS/GNSS receivers. If you look at the power levels at the ground of the important GNSS/L-Band signals you'll see that even after the fall off of the GPS filter they are still swamped by the LightSquared signal. 



Also, I forgot to mention in the original posting that the traditional use of the spectrum occupied by the new LightSquared service was for Mobile Satellite Systems (MSS) which has a low power envelope like the StarFire/OmniSTAR signal on the graph.

The reason why GNSS receivers use such a wide filter is that each satellite navigation system has its' own allocation of spectrum.

To receive GPS L1 you must be sensitive to the signal centered at 1575MHz. 

GLONASS is carried at 1575MHz (L1 again) and frequencies that range from 1595MHz, to 1609MHz.  

It was most convient for vendors to design their L1 filter in a manner that gave them a flat response all the way from the center of L1 out to the far edge of GLONASS's ~1600MHz signal. When this filter is mirrored on the lower frequency side of the L1 center this results in a very wide and flat filter.