Actually it is setting in earlier than I thought. Usually by year 6 the president is functionally irrelevant. If he loses sequestration he becomes irrelevant much earlier than that.
Because he's such a novice and convinced of his own superiority, I am certain that a) Obama was convinced he couldn't lose the sequester fight and b) didn't realize how much political capital he was staking on an unimportant fight. (Of course, we have yet to see if he will suffer any loss of credibility after he loses... IF he loses. I have a great deal of faith in the ability of the Republicans to screw this up.)
The "cool" people voted for Obama this time only because they were convinced McRomney was the DEVIL. *(Sort of the same as: we don't have a plan, we just don't like your plan) They didn't vote FOR Obama this time. I don't think the Obama's realize that.