Crass, but inevitable. In the wake of the killing of Osama bin Laden, media and pollsters rushed into the field to insta-poll public reaction. Taken together, Pres. Obama is seeing a significant boost in numbers on handling terrorism and the situation in Afghanistan. However, the overall “Osama bounce” for his general job approval numbers looks below average so far.

Let’s start with the WaPo/Pew figures:

Barack Obama’s job approval rating has jumped in the wake of bin Laden’s killing. In the one-day survey, 56% say they approve of the way Obama is handling his job as president while 38% disapprove. Last month, Obama’s job rating was about evenly divided — 47% approved, 45% disapproved. Obama has gotten about the same boost in job approval as did former President Bush in the days after the U.S. military’s capture of Saddam Hussein in December 2003. Following Saddam’s capture, Bush’s rating rose from 50% to 57%. (A more comprehensive survey will be conducted May 5-8 to follow up on these preliminary reactions to the death of bin Laden and Obama’s job performance.)

However, while Obama’s ratings for dealing with the situation in Afghanistan and the threat of terrorism have improved dramatically — by 16 points and 14 points, respectively, since January — opinions about his handling of the economy have not. Just 40% approve and 55% disapprove of his job performance on the economy, which is little changed from April.

Obama gets far more credit from the public than does George W. Bush for bin Laden’s killing. But the military and the CIA and other intelligence agencies receive much more credit — fully 86% say the U.S. military deserves a “great deal” of credit and 66% say the same about the CIA and other intelligence agencies.

Roughly a third (35%) say that Obama deserves a great deal of credit for bin Laden’s demise, and a large majority (76%) says he deserves a great deal or “some” credit. By comparison, 51% say that Bush deserves either a great deal (15%) or some credit (36%) for the death of bin Laden.

On the other hand, the CNN/Opinion Research Corporation poll released Tuesday showed a statistically insignificant one point rise in the president’s overall approval rating compared to a poll taken over the weekend. Based on the historical data below, I would tend to favor the WaPo’s 9% boost — but the NewsBeast poll also showed no change in Obama’s overall approval rating (there is good news for him in some of the NewsBeast internals, including perception as a leader and head-to-head matchups against GOP rivals).

How do these numbers stack up against past bounces? Glen Bolger of Public Opinion Strategies has a handy chart stretching back to Pearl Harbor, noting that — excepting the unusually large 35% bounce George W. Bush got following 9/11 — the bounce from this sort of event averages 13% for about 22 weeks. Bolger’s numbers are not directly comparable, as they come from Gallup. Oddly, Gallup did its own quickie poll, but did not release job approval numbers for Pres. Obama. However, the Gallup numbers on awarding credit are quite similar to the Pew numbers, so I would be surprised if Gallup shows much more of an overall approval boost than Pew does (more numbers are due tomorrow). Assuming this for the moment, Obama’s overall poll average seems unlikely to move more than a few points.

What do these numbers mean politically? Stephen Hayes and David Corn — who probably do not agree on much — both think the numbers are pointless and that what really matters is whether the GOP charge that Obama is weak on defense is now useless. That is an important point, but probably not the whole point, for at least three reasons. First, we have no way of knowing what other foreign policy or war news may crop up between now and November 2012. Second, as George H.W. Bush learned in 1992, after a war bounce fades, the election may turn more on the economy and the deficit. Third, in the short-term, a boost in job approval could help Obama on non-war issues. After a midterm shellacking, Bill Clinton’s handling of the Oklahoma City bombing helped change the perception of his presidency, which in turn helped him confront the GOP over the budget (and that was after a mere four point bounce of shorter duration). Obama probably hopes the same sort of dynamic will help him now, but the early numbers suggest he may be disappointed.