(Andrew Harrer/Bloomberg)

But you know that every time you do that, you make it impossible for members of the other party to support you. Maybe you’ve seen this graph, and maybe you haven’t. But you know full well that presidents polarize. That you polarize. If you take a strong position, the other side will immediately take the opposite position. And in the American political system, you need the other side.

This is what I’ve come to think of as the Paradox of Presidential Leadership, and it’s in full display with the Gang of Six. When, in the State of the Union and the 2012 budget, the Obama administration didn’t fully embrace the Simpson-Bowles framework or release an alternative proposal of their own, commentators on both sides of the aisle were furious. “He punted to a fiscal commission and then he just didn’t even embrace the Fiscal Commission,” Paul Ryan told Fox News, conveniently ignoring that he had served on the fiscal commission and then voted against the final report.

White House officials protested that they had signaled in every way they knew how that they wanted to begin bipartisan talks leading to a grand bargain. “If you look at the history of how these deals get done,” Obama said in press conference on his budget, “typically it’s not because there’s an Obama plan out there; it’s because Democrats and Republicans are both committed to tackling this issue in a serious way.” But this was taken as a lame cop-out. If the White House wanted to address the issue, it would have come out with a plan, or endorsed someone else’s plan.

So now, a bipartisan group of senators has emerged with a grand bargain and the White House has voiced its support. It’s exactly what everyone in Washington said they should do. And how it’s playing out? Well, here’s what led Mike Allen’s Playbook this morning:

— A Senate Republican leadership aide emails with subject line “Gang of Six”: “Background guidance: The President killed any chance of its success by 1) Embracing it. 2) Hailing the fact that it increases taxes. 3) Saying it mirrors his own plan.”

I see no reason to believe that Senate Republican leadership aide is wrong. But if Obama hadn’t announced his support for the Gang of Six, that aide would be e-mailing: “Background guidance: Leaks from White House negotiations aside, the President has now dismissed every actual budget proposal that’s been put in front of him. Tell me again how serious the White House is on the debt?” And all the D.C. sages would be nodding sagely.

In the end, the problem for the president is that though the public sees him as the player with the responsibility to make a deal, there’s not much he can do to persuade the opposition party to cut a deal it doesn’t want to cut. In the words of Allen’s Senate aide, going public “kills the deal” because it becomes associated with the president, and the opposition party is not supposed to associate with the president. Not going public kills the deal because it doesn’t create any pressure on the opposition party to bargain. But the reality is that nothing here is killing a deal. The deal was never alive to begin with.