WASHINGTON — Republican nominee Mitt Romney faces a fundamental problem as the presidential campaign moves into its final phase: Voter attitudes about the state of the economy have begun to improve, and enthusiasm about voting has risen among key blocs of Democratic-leaning voters, particularly Latinos.

Since the beginning of the campaign, one assumption has served as the foundation for Romney’s campaign: that voters deeply upset over the state of the economy would want to fire the incumbent enough to push aside any concerns about his challenger.

To describe the state of mind of voters he encountered in focus groups this election cycle, Republican pollster Whit Ayres has used the metaphor of a parent searching for a surgeon to treat a grievously ill child. Faced with such dire need, the parent would have no interest in anything other than the surgeon’s skill with the knife, he said.

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Unfortunately for Romney, just when it would matter most, that metaphor may no longer fit. Attitudes toward the economy have warmed in recent weeks. Measures of consumer confidence have begun to tick upward, voter outlook about future conditions has brightened after a slide during the summer, and the percentage of Americans who feel the country is on the “right track” has risen steadily — albeit slowly.

At the same time, some Democratic-leaning groups whose enthusiasm about voting had lagged now appear to have started to focus on the campaign. The most noticeable shift has taken place among Latinos, whose enthusiasm about voting, along with their tilt toward President Obama, has grown substantially since the Democratic convention.

For Romney, such shifts in basic voter attitudes form a hurdle that’s far more serious — and more difficult to turn around — than a week of unfavorable headlines on the campaign.

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None of that means the election results are a foregone conclusion. “We’ve still got a majority of the country either thinking we’re on the wrong track or dissatisfied with the direction of the country,” Ayres said. So long as that’s true, “the incumbent president remains vulnerable,” he said, adding that whether he’s vulnerable enough is the question the election would test.

The evidence for voters growing less worried about the state of the economy and the nation in general comes from a large variety of surveys. The Thompson/Reuters University of Michigan index of consumer sentiment rose sharply this month — catching forecasters by surprise. Gallup’s measures of economic confidence have similarly increased steadily since late August.

Another set of measurements comes from a question that polling firms have asked voters for years about whether the country is going in the “right direction” or headed down the “wrong track.” To take one recent example, an NBC/Wall Street Journal survey released this month found 39% of voters saying the country was headed in the right direction. While that’s hardly a ringing endorsement, it was the most positive rating the poll had found on that question since Obama’s first year in office.

Partisanship plays a role in such measures — Democrats and, to a lesser extent, independents have grown more optimistic about the economy while Republicans have remained much more grim. So part of the improved view of conditions reflects greater partisan enthusiasm. That same partisan enthusiasm also shows up in measures of Latino voters.

A weekly survey by the polling firm Latino Decisions for ImpreMedia, the owner of several Spanish-language newspapers, shows that over the last four weeks, Latino voters’ support for Obama, already high, has risen by a statistically significant amount. More significantly, enthusiasm about voting, which often presages turnout, has gone up sharply.

Obama and his campaign have “worked pretty tirelessly to improve their image,” said Stanford University political science professor Gary M. Segura, one of the founders of Latino Decisions. “They’ve taken a somewhat dispirited electorate and energized them.”

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Republicans have put considerable hopes in the series of presidential debates scheduled to begin next week, knowing that debates tend to favor the challenger, if only a little, just by putting the candidates on equal footing, side by side on the same stage.

But for all the attention they get, “when it comes to shifting enough votes to decide the outcome of the election, presidential debates have rarely, if ever, mattered,” George Washington University political science professor John Sides wrote recently.

In the 1980 campaign, for example, a race often cited as one in which a debate proved decisive, Ronald Reagan already led Jimmy Carter before their single encounter, although his lead in polls widened thereafter.

For now, Obama appears to hold a 3- to 4-percentage-point lead nationally and a corresponding — and in some cases slightly larger — advantage in the states that could swing either way. Since the start of last week, a variety of polling organizations has released 37 separate swing-state surveys; Romney led in only four of them, three by the same pollster.

Since modern polling began in the 1940s, the only example of a candidate who won the popular vote after being behind in public polls at this stage of the race is Harry S. Truman in 1948.

david.lauter@latimes.com