I'm wondering how a backdoor in a random-number generator (as rumored the NSA have placed), actually compromises the security of things like VPNs or TSL/SSL.

What I understand is that, if such a backdoor exists, then after observing a certain number of pseudorandom bits, the attacker can then predict the rest of the pseudorandom sequence. 

Can someone walk through the steps of how this allows an attacker to actually read encrypted packets?  For example, how would an attacker get access to the first N random bits of a pseudo-randomly generated key in the first place.  Is the problem that any random key is effectively only N bits long because if an attacker guesses the first N correctly, he can generate the rest of the key using the backdoor?  Or is it something more complicated.