The Congressman could very well be right. If he represents a state or district that has A LOT of applicants for SAs (like San Antonio TX, Colorado Springs, CO or the DC area) then he will have to carefully choose who gets his nomination. This process suggests the candidate he chooses is likely to be HIGHLY qualified for an SA. Conversely, if he represents a state or district that has just ONE applicant for SAs, like a remote mountainous district in Montana or North Dakota, then to ensure SAs (and the military) are representative of the US population, that applicant will be accepted by the SA as long as they meet minimum qualifications. This sets up a weird outcome where by a minimally qualified candidate from Montana gets in while the second best candidate from San Antonio (who might be very nearly as highly qualified as the #1 candidate) does NOT get in. This is why you should try to obtain as many nominations as possible.
As to how long it would take, I do not know if the kind of situation above is flagged early to accelerate a "sure thing" decision. My guess (and this is pure conjecture) is it will NOT to ensure everyone's package is fully considered so applicants can be ranked with specific nominations applied (when more than one is available) to produce the best overall entering class. Also, it prevents candidates from assuming they received an early offer because they are highly qualified when in fact they might have been minimally qualified.