The Everest-size electoral challenge facing President Obama is encapsulated in a single question in the latest Washington Post/Bloomberg poll: Would the economy be better or worse if a Republican were elected president in 2012?

There are three interesting aspects to the answers: the overall result, the divided state of Democratic voters, and the even more skeptical attitude of independents.

On the basic question, nearly half of those polled (45 percent) believe the economy would be the same no matter whether a Republican or Democrat is in the White House.

This conclusion is not unreasonable. A president’s ability to bring about short-term improvements in the economy is limited, even if he could wave a magic executive wand and see his program instantly enacted. In the current, gridlocked environment — see, for example, the debate over the president’s jobs package — presidential power is even more constrained.

The paradox for voters is that at the same time nearly half don’t believe a president will make a difference, the economy is at the top of their list of concerns.

One possibility is that voters will base their choice on other issues or stick with their party allegiance, if they have one. Another, which seems at least as likely, is that they will decide that Obama has had his chance and that someone else deserves a try.

Which leads to the second aspect of the answers: the division, even among Democrats, about whether the economy would be worse if Obama were to lose. Almost half (48 percent) said it would be worse, but the number who believed it would be the same was nearly equal (44 percent).

The split among Republicans was far sharper: 63 percent thought the economy would be better if a Republican were elected president while only 29 percent believed it would be the same.

This striking difference both reflects and explains the enthusiasm gap between Democratic and Republican voters this election. The voters of one party — Republicans — think the outcome matters much more than do voters on the other side. This does not bode well for Democratic turnout.

The key to the election, of course, will be independent voters, about one-third of the electorate. In the Post/Bloomberg poll, independents were markedly more skeptical about whether a different president would make a difference for the economy.

A clear majority (55 percent) said the economy would be the same with a Republican president. The rest were closely split, with 17 percent thinking a Democratic president would be better for the economy and 19 percent saying a Republican would be preferable.

The fundamental challenge for Obama is to convince these swing voters that, despite their current concerns about the economy, his re-election would make a difference — or at least that the other candidate would be worse.

He faces an uphill battle. In 2008, independent voters favored Obama over John McCain by a margin of 52 percent to 44 percent. Now, according to a new poll by the Pew Research Center for the People and the Press, independents favor former Massachusetts Gov. Mitt Romney by 13 points, 54 percent to 41 percent.

The Obama campaign argues that it can turn this situation around — indeed, that it is already doing so. In a memo released by the campaign Tuesday, adviser David Axelrod cited polling showing increased support for the president’s jobs package: “Trust in creating jobs has gone from a tie in early September to a 15 percent advantage for the president. And among independents, Republicans have gone from a 5 percent advantage to a 13 percent disadvantage.”

Having spent an evening last week watching, via video hookup, focus groups of “Walmart Moms” in Florida, New Hampshire and Iowa, I have no doubt that voters are despondent about the economy and fed up with their politicians.

Even those who supported Obama in 2008 were disappointed in his performance; some who did not vote for him expressed sympathy with his plight. But they reserved their greatest exasperation for Congress, which, as one New Hampshire woman put it, is “playing a game of dodgeball.”

Obama may want to run, Truman-like, against Congress. But he also told voters three years ago that he was the one to stop the dodgeball.

Having failed, however predictably, he must now convince voters that he deserves more time and that his solutions are better. That may be true — but, as the poll suggests, it will also be a hard sell. 

Ruth Marcus is a columnist for The Washington Post. She can be contacted at:

ruthmarcus@washpost.com