President Obama has accomplished more in two years than could be expected by most Presidents over two terms. So what if for the next two years, the President accepts all the Republican ideas to cut taxes and cut the budget and only trims them when they're "really extreme"?
First, if he signs an extension of all the Bush tax cuts, cuts the budget in a way that can't be denied, continues to puruse a center-right foreign policy, and in general is not combative, he can claim centrist credentials.
What does the left get?
Obama and the Democrats get to keep all of the acheivements from the first two years. Financial reform stays. Health reform stays. And so on. The President can then accept common sense tweaks and minor changes.
It would be nonsense( though they still would try) to say how extreme the President was when he accepted 70-80% of the Republican ideas. If he didn't raise taxes, if he did cut the budget, and so on.
Democrats in Congress could force Republicans to get all the votes. They then can run against both Republicans and Obama. So redstate Democrats would have a moderate record to win on. Blue state Democrats could run against the Republicans who cut education, etc.
I wouldn't choose this path because it's too cute by half, and too much defense. I would choose to go and stay on offense. In addition, even if this is the plan, the President should puruse his own aggressive ideas and then compromise to this rather than starting out at a middle point. It's negotiation 101. The President is too honest in his willingness to work together. You don't get points for where you start out. Regardless of the facts, people assume you are posturing and expect you to give some more. You're much better off being "extreme" and then accepting reality later.