The public will never know what went on behind closed doors in the legislative and executive branches, and that includes who uttered the word "sequester" first. In a way it's as silly as the Benghazi argument about who said "terrorist" first (or any other magic word that whips up indignation -- pick your favorite).
In the case of the sequester, it got approved (by both parties, ultimately) pretty much because nothing else could. The tea party Republicans leveraged their power in congress without regard for the consequences to the economy and the citizens. If they believed they were really doing something good, they'd be claiming right now that they started it.
Arguing about the historical trivia of the sequester is a deliberate distraction from the what's really important: what happens next. The Republicans (the insane ones, I mean) want to proactively pin all possible blame on Obama and the Democrats when the sequester causes an economic slowdown and negative effects on individual Americans' lives.
I see no reason to even engage in the "who started it" discussion. It's a fake.
If there are any causal agents we ought to be dealing with, they're structural. The rules the Senate oparates under prevent its functioning in a rational parliamentary manner, for starters. So is gerrymandering and the laws and customs that make it so convenient. What else?