Here's how Martin summarizes Reichenbach's argument:
1. A contingent being exists.
a) This contingent being is caused either (i) by itself or (ii) by another.
b) If it were caused by itself, it would have to precede itself in existence, which is impossible.
2. Therefore, this contingent being (ii) is caused by another; that is, it depends on something else for its existence.
3. That which causes (provides the sufficient reason for) the existence of any contingent being must be either (iii) another contingent being or (iv) a noncontingent (necessary) being.
c) If (iii), then this contingent cause must itself be caused by another, and so to infinity.
4. Therefore, that which causes (provides the sufficient reason for) the existence of any contingent being must be either (v) an infinite series of contingent beings or (iv) a necessary being.
5. An infinite series of contingent beings (v) is incapable of yielding a sufficient reason for the existence of any being.
6. Therefore, a necessary being exists. 
Now, Martin levels multiple objections against Reichenbach's argument, but the one that stood out to me most was this one:
"One can . . . [argue] that the totality of contingent beings is itself contingent on the contingency of that that make up this totality is to commit a composition fallacy. . . . Just because each individual being could cease to exist, it does not follow that all could cease to exist at the same time." 
The problem with such an objection is that it leads to obvious absurdities. Is it, then, necessarily the case that some contingent thing or other exist? As Pruss is apt to ask, would the non-existence of all non-unicorns imply that a unicorn exists? Surely not. It's at this point in his critique that I think Martin takes a much too liberal use of what we call the composition fallacy. If every part of a mountain is made of rock, then the mountain as a whole must be made of rock. Likewise, if every part of the totality of contingent things C is contingent, then C must also be contingent. While I respect Martin's intellect, I think he's just grasping at straws with this objection.
 Michael Martin, Atheism: A Philosophical Justification, Temple University Press, 1990, p. 119.
 ibid., pp. 122-123.