psloss - you asked for it:
The short answer is sometimes!!! When it comes to contingecy aborts there is no simple answer. There are just too many variables invovled such as how many engines have failed, when did they fail, are there other systems problems or flight control issues. If a an engine or APU comes apart in the back end of the orbiter it is likely that many other systems will be involved.
Shuttle Ascent trajectories are designed in such a way that from liftoff to MECO (main engine cutoff) if one engine fails there is always at least one CERTIFIED abort option. Those are AOA, ATO, TAL, and RTLS...pretty much in that order of preference for a performance problem (i.e. loss of thrust). The priorities can be different for systems problems such as loss of APUs, electrical bus failures, themal window pane breached etc.... In many cases the shuttle can loose two engines and still use one of these abort options. However there are significant portions of the trajectory where the loss of 2 or more engines will result in a contingecy abort, particularly in the early parts of the Ascent. Among these are so called black zones meaning they are not expected to be survivable.
The stated purpose of a contingency abort is to guide the orbiter to a safe gliding flight condition where a bailout or landing can be performed.
Abort boundaries are based on inertial velocity in feet per second. These boundaries are slightly different for every launch do to changes in variables such as vehicle weight, inclination, etc..
Getting back to the question of ECALs (east coast abort landings) which is a form of contingency abort: Using rough numbers from the STS-114 mission I will give you an example.
If you launched in the center of the launch window and had a two engine failure at a velocity of lets say 5,300 feet per second you could attempt an ECAL to Wilmington. This failure is so early in the Ascent (just after SRB sep) that TAL is not an option, in fact you havent even made it to the first TAL boundary which is at a velocity of 5,800 fps, and would only get you to Morone in Spain under a single engine failure scenario. Since we have lost two engines we are in a contingency abort situation at this point and the only potential landing site is Wilmington (disregarding contingency RTLS scenarios). The problem is the failure happend so early that the odds of making the runway at Wilmington are not good (the checklist actually has a little note that says "bailout in this region is probable")

But if things worked out just right you could theoretically make it all the way:) Now if these two engines failed a little later, lets say at a velocity between 6,800 and 7,300 you can now choose between Wilmington and Cherry Point. You are solidly in the Wilmington boundary now, in fact that unpleasant little warning in the checklist is now gone... Well its not completely gone, because if we are at the early part of this boundary (ex: 6,800 fps to 6,900 fps) then an attempt at Cherry Point is regarded as a probable bailout region. Between 6,900 and 8,100 you would be in the heart of the Cherry Point window and that nasty little warning is gone again. Yet even without that warning there is no gaurantee you will make the runway.
I have only listed a couple of the tiny little windows here and only two of the 13 or so ECAL runways and yet the scenario was still pretty complex. In reality you have to consider the condition of the launch vehicle, the amount of energy you have (in terms of velocity), whether or not you launched at the opening, middle, or end of the launch window... Add to that potentially bad weather at your selected landing site. Launch rules don't evalluate weather at the Contingency sites because the failure modes that would get you there are considered to be relatively remote (i.e. it would take multiple failures) and there are so many sites that if weather had to be good at all of them you would never be able to launch. Just think of how many times we couldn't launch becuase of the 3 TAL sites not one of them had good weather.
Mark