A new Washington Post-ABC News poll shows President Obama’s approval rating, which increased in the wake of the killing of Osama bin Laden last month, has dropped back to the same level it was before one of the most important events of Obama’s presidency.

Here are some other findings from the survey and how they might affect Obama’s reelection chances.

What’s good in the poll for Obama:

1. His approval, while down from its post-bin Laden high, is at 47 percent. He can certainly win reelection next year with a number in that range: President Clinton had a similar approval rating this time in 1995.

2. Early national polls are not always great at predicting election results. But pitted against nearly every potential GOP candidate, Obama would be suppprted by a majority of voters.

What’s bad:

1. The poll shows Obama is in a dead heat with former Massachusetts governor Mitt Romney in a potential match-up (49 percent for Romney to 46 for the president).

That suggests Romney, despite the baggage of his defeat in 2008 and controversial health care bill he signed in Massachusetts, would be a formidable opponent for the president. The poll also suggests the Massachusetts health-care bill may not kill Romney’s chances of winning the GOP nomination; a majority of Republicans either don’t know enough about it to have an opinion (37 percent) or at least somewhat support it (21 percent). (These numbers could both go up if other Republican candidates make attacking that law a centerpiece of their campaigns.)

2. Sarah Palin’s dismal numbers (more than a third of Republicans said they would not consider voting for her in a GOP primary) suggest she has little chance to be the Republican nominee. Democrats would love for her to be the candidate, as they think independents would flock to Obama and liberals would turn out in huge numbers to defeat her.

What’s ugly:

1. Since the start of this year, Obama has argued the growth in

private sector jobs and declining unemployment show the economy is

recovering. Voters don’t believe him. Fifty-nine percent disapprove of his handling of the economy, 57 percent don’t think the economy has begun to recover, and among those who do see a recovery, fully 81 percent think it has been “weak.”

Obama today

Obama on Tuesday will host German Chancellor Angela Merkel at a series of meetings at the White House and then at a state dinner.

The official reason for the visit is to present Germany’s first female chancellor with the Presidential Medal of Freedom, which Obama awarded Merkel in 2010.

But the meeting also could help smooth over disagreements between the two leaders, particularly on the NATO military intervention in Libya, which the U.S. backed but Germany opposed. Last year, Merkel shot down Obama’s calls for increased spending by Germany and other countries in Europe to help spur the the global economy.

It will be the fourth state dinner Obama has held as president. He hosted the leaders of China, India and Mexico earlier in his term.

Polling director Jon Cohen and polling analyst Peyton M. Craighill contributed to this report.