As I have just written my thesis on the future of long range operations...Wino has it right IMO, the principle issues are not related to engine reliability. Double engine failure from independent causes is highly unlikely, whereas common cause failures are a) more frequent and b) just as likely to occur aboard a twin as a 3 or 4 engine a/c.
What I find concerning is the push by manufacturers for diversion times " to the limit of the aircraft's most time limited system" LROPS, as proposed by Airbus, might allow for direct flight over Antarctica from South America to South Africa and Australasia. Such flights would involve diversion times up to 8 hours (apparently). Anyone fancy flying 8 hours with a cargo fire?
There are also the usual arguments surrounding "adequate" and "suitable" diversion airfields etc. but the upshot is that the number of engines is less important than it used to be.
HOWEVER..ETOPS and it's succesors (which will probably be called ETOPS btw) should have safety as the primary driver. ETOPS207 in the North Pacific is (IMHO) the first time ETOPS was extended primarily for economic rather than safety reasons. This sadly has given ammunition to those who claim that the FAA sometimes acts as marketing department for U.S industry. This is a shame as the conclusions of the ARAC ETOPS working group are generally quite sound.