One of the primary legal arguments being used to support random searches of individuals on NYC subways is Michigan State Police Dept v. Sitz, where Sitz argued unsuccessfully that sobriety checkpoints were unconstitutional.
The Court noted that "no one can seriously dispute the magnitude of the drunken driving problem or the States' interest in eradicating it," and that "the weight bearing on the other scale--the measure of the intrusion on motorists stopped briefly at sobriety checkpoints--is slight." The Court also found that empirical evidence supported the effectiveness of the program.
Using random subway searches to prevent terrorism, however, is not supported by any empirical evidence. Even targeted public searches of suspicious individuals have never been shown to prevent terrorist attacks in the U.S.
Similarly, the chance of dying through terrorist bombings in the U.S. is statistically slight in comparison to those killed by drunk drivers. Approximately 25000 people are killed each year in alcohol related accidents, whereas fewer than 500 people are killed per year in the U.S. from terrorism. That's 1/50th the risk of death, which is certainly a disputable magnitude. Lower than those who die from drugs, or guns, or even stabbings.
As for the circumstances, there are no special extenuating circumstances that would make regular random searches of our public subways a daily necessity, any more than searches of all cars going across bridges or in tunnels, or even cars going through a potential roadblock. All of the above are on public property.
In comparison, when you stop cars for a sobriety checkpoint, the timing and location is generally specific to those times most frequented by drunk drivers, and for every hundred or so people who are minorly inconvenienced, one drunk driver is taken off the road. What New York is proposing, however, is inconveniencing hundreds of thousands of people with the strong likelihood of finding no terrorists whatsoever.
Finally, when you start targeting all large bags as being "suspicious" bags, then you also establish a precident that could equally be applied to possible suicide bombers.
In other words, if you buy NYC's legal argument, then you should also believe that all of these potential suicide bombers should be stripsearched too.