For my part, for example, I have met various relatively low level Norwegian politicians and trade union people that have huge networks. These low level politicians, for example have met people with vastly more influence, such as Castro (communist politician who moved to Cuba; these days he's converted to Islam, become a social democrat, and runs a shipping company in Norway..), Mao (trade union guy who has a picture of himself with Obama from some meet and greet in the 60's), Obama (hand shakes during some visit), the new secretary general of NATO (he's ex-Norwegian prime minister for the labour party - every member of parliament in recent years and most Labour party members have met him, so most Norwegians will only have one step between them and him), the Dalai Lama (large numbers of Norwegian politicians have met him), just to mention some random names, though most of them will have done little more than shake hands.
Extend it one level, and the people I know will have worked closely with people who have worked closely with the people mentioned.
Most people will be able to find paths to someone that the NSA could use to justify surveillance if they want to in 3 degrees or less. Of course, in most cases these people will not have discussed anything that would give the NSA a legitimate reason for interest.
So the 3-degrees thing basically amounts to saying they can conduct surveillance of everyone they bloody well please, as long as they can be bothered to identify a suitable connection.