For all their concerns about the economy as a top election issue, American voters don't have huge expectations of what the occupant of the Oval Office can do to steer a better course on things like jobs and GDP.

That's a central message from a new Associated Press/GfK poll that's in the news Monday.

In reporting its survey of US adults, the AP encapsulated the story in this headline: "Poll: Half doubt next president will alter economy." The story has been picked up by various news organizations Monday, and there have been blogs about it, under similar headlines.

So, wait a minute. Is this poll really telling us that the 2012 presidential election – billed as an epic battle between President Obama and Mitt Romney over the nation's economic soul – is essentially meaningless?

Far from it, really.

The grain of truth in the AP headline is that fewer than half of Americans (48 percent) say the election outcome will have "a great deal" or "a lot" of impact on the economy. And history suggests some justification for that view. A president is just one part of the federal government, after all, and the federal government is just one influence on the vast web of consumers and suppliers known as the economy. Most citizens know that.

But here's the important caveat:

Federal policies do matter for the economy, and citizens know that, too. Where the AP story played up the fact that "only" 48 percent of respondents see the election having a significant influence on the economy, the number of people in the poll who said the election won't make any difference was much smaller: just 7 percent.

Here's the way the answers broke down in the poll, which was taken June 14-18.

When asked about the election's expected impact on the economy, 7 percent said they expect none at all, 17 percent said "a little," 26 percent said "just some," 18 percent said "a lot," and 29 percent said "a great deal." So the largest cluster of responses actually came on the end of the spectrum viewing the election as very consequential.

When the poll diced the question into smaller parts – on health care, unemployment, and the federal budget deficit – the responses ran along much the same lines. The next president will influence health care a bit more than he will influence the overall economy, they predict, and he will influence unemployment and deficits a bit less.

Again, AP staked out one valid point: Many Americans are rightly skeptical of how much one person can do, even someone sitting in the Oval Office.

Consider another recent poll, conducted by Princeton Survey Research Associates International for the financial firm Bankrate.com. The survey found that 21 percent of Americans think an Obama victory would be best for their personal pocketbooks, an equal percentage favors Mr. Romney, while fully 50 percent "don’t think it will make much difference either way," Bankrate reported.

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At the same time, all signs point toward the economy remaining a vital campaign issue – with the two main candidates staking out considerable contrasts on how they would approach economic policy. Mr. Obama hopes to tax the rich more, while Romney says he wants them to pay about the share of overall US income taxes that they do now, to give just one example.

And all signs suggest that when the election is over, the White House occupant will influence important choices the nation faces on matters including taxes, federal spending, entitlement programs, and the regulation of health insurance.