The death of Osama bin Laden may not have much of an effect on the 2012 presidential campaign, but it’s far more likely to help Barack Obama get things done this summer and perhaps continue to help him down the road.

Presidential scholar Richard Neustadt wrote about two assets that could help a president influence those he deals with: professional reputation and public prestige. In both cases, what matters is what Washingtonians think – in which “Washingtonians” are people whom the president deals with, whether they are actually in Washington or not.

Political leaders care about presidential popularity among the public at large, but more importantly to the constituencies they represent. And most Washingtonians, whether they are members of Congress, interest group leaders, or even foreign governments, have particular constituencies they need to keep happy. On one level, this is easy: To the extent that Obama rallies in opinion polling, his public prestige will improve. To Neustadt, higher prestige works by giving the president what he calls “leeway” — basically, when the president is riding high, it gives him a bit of a negotiating advantage with everyone. I’d add that there’s only a rough correlation between public opinion polling and what people inside the Beltway perceive to be the president’s popularity; in my view, Washingtonians probably overstated his popularity during his first few months, but understated it during much of the last year. If, as I and others expect, the actual polling bump is short-lived, it could still help Obama somewhat in the future if Washingtonians over-adjust, at least until the next major event comes along.

Professional reputation is, more or less, how political elites believe the president handles his job. Do they trust his word? Do they believe that he rewards friends and punishes enemies? Do they believe that he knows what he’s doing — that he’s a winner? How they behave in negotiations with him, or in any actions in which presidential reactions are important, is, for Neustadt, powerfully affected by those expectations. And it seems to me that this kind of event can really change (and, given the event, for the better) everyone’s views of Obama.

This kind of thing can really matter! In 1995, Newt Gingrich, by all accounts, fully believed that Bill Clinton was a weak man who would fold under pressure, and proceeded accordingly. Of course, he learned otherwise, but the point is that the government shutdowns of 1995-1996 were in large part a direct result of Clinton’s various and many defeats in 1993-1994. Obama made it through his first two years with (as best as I can tell) a better professional reputation than Clinton had in 1995, but I do think bin Laden’s killing is likely to further solidify things — it’s going to be a while before anyone thinks of the Obama White House as a gang that couldn’t shoot straight, or doesn’t believe this president is cool under pressure, or that he doesn’t have what it takes to pull the trigger when he needs to. Figuratively, that is.

None of that guarantees that Obama will get his way in budget negotiations, or in squabbles with executive branch agencies, or with leaders of foreign nations. But it should help, perhaps quite a bit.