Obama is getting a lot of flack for agreeing to a two-year wage freeze for federal employees.  “Why give away a negotiating chip?” ask the commentariat, “and with nothing in return!?”  Or as Kevin Drum put it:  “Obama has another two or three weeks to prove he’s not an idiot.”

Actually, there are three solid political reasons to freeze federal pay (even if the policy wisdom is debatable). First, it means he (not Republicans) get credit for something likely to be popular politically; Second, he shows he is capable of taking decisive action; Third, and most important, if he wants to negotiate successfully in the future, he’s going to need to rebuild his popularity.

In short: the pay freeze decision makes sense if you think of it not as a preemptive good-faith giveaway, but as a moment of leadership aimed at rebuilding public approval and all the bargaining power that goes with it.

Richard Neustadt’s classic Presidential Power offers this pithy aphorism: “Presidential power is the power to persuade.” By which he means not personal charm and clever argumentation, but a power that comes from public popularity and reputation. A president esteemed by the people and regarded as competent is in a significantly better negotiating position than one who isn’t. What Neustadt understood is that bargaining depends much more on public prestige than on the individual chips.

We just had an election in which big government was a starring villain, in which real concerns were expressed about runaway federal spending, and in which many swing voters lost faith in the Democrats. Obama is now preparing for a two-year battle in which he and the Republican leaders are both going to be appealing to the American public in a popularity contest that will determine who has to give in and how much.

Freezing federal pay for two years is a small move, but it’s a symbolic move. It signals that Obama understands that the public is unhappy with the size of government, and that he is doing something decisive about it.  It also shows he is acting as a leader.

By contrast, if Obama had ultimately frozen federal pay after Republicans had pressured him into doing so, you can be sure Republicans would be claiming all the credit, and would be spreading the narrative of Democratic capitulation.

The latest Gallup poll puts President Obama’s approval rating at 45 percent, and his disapproval rating at 47 percent, more or less where it has been since June. Not terrible, but not great, and right now about equivalent with John Boehner (41 percent favorable, 39 percent unfavorable) and Mitch McConnell (38 percent favorable, 36 percent unfavorable).

On the big issues ahead – well, basically taxes and deficit reduction are probably going to dominate the agenda – there are not only going to be two competing arguments, but two competing spokespeople making those arguments.

Republicans have demonstrated time and again that they are not interested in playing nice and engaging in the sort of polite bargaining chip negotiations that many commentators seem to want Obama to conduct. All indications are that they are not particularly interested in compromise, and are probably willing to do what it takes to pummel Obama and the Democrats into accepting complete tax cut extensions and massive federal spending cuts.

Essentially, this leaves Obama with two choices. One is to continue to operate in good faith, proposing reasonable fig leafs, and let Republicans continue to take the fig leafs and offer nothing in return because they don’t feel they have to. This makes Obama look weak and ineffectual, and also allows Republicans to claim equal credit for any popular compromises.

The other choice is to show some leadership and build back public support with issues designed to win back lost swing voters. Some on the left might call the federal pay freeze a milquetoast bipartisan compromise. But Obama can and should call it taking the initiative and a way to shift the narrative. He needs to say: “I’m listening to the American public, and I’m taking decisive and smart action to limit federal spending and getting the government’s fiscal house in order. I know you are concerned about our long-term future, and so am I. I get it. If Republicans want to put petty politics aside and work with me, I welcome their input and partnership. But if they’re more interested in posturing, then I’m going to take care of business without them.”

Choice one is doing the same thing over and hoping for a different result, which is one popular definition of insanity. Choice two is a gamble. It may not work. But right now it’s the best gamble he’s got.