WASHINGTON (Reuters) - Democrat Barack Obama has a 7-point lead on Republican John McCain in the U.S. presidential race, and holds a small edge on the crucial question of who would best manage the economy, according to a Reuters/Zogby poll released on Wednesday.

More than a month after kicking off the general election campaign, Obama leads McCain by 47 percent to 40 percent. That is slightly better than his 5-point cushion in mid-June, shortly after he clinched the Democratic nomination fight against New York Sen. Hillary Clinton.

But Obama’s 22-point advantage in June among independents, a critical voting bloc that could swing either way in the November election, shrunk to 3 points during a month in which the candidates battled on the economy and Obama was accused of shifting to the center on several issues.

Obama had a 44 percent to 40 percent edge nationally over McCain on who would be best at managing the economy, virtually unchanged from last month. Among independents, the two were tied on the economy.

“There has been a real tightening up among independents, and that has to be worrisome for Obama,” pollster John Zogby said. “It doesn’t seem like Obama is coming across on the economy.”

The economy was ranked as the top issue by nearly half of all likely voters, 47 percent. The Iraq war, in second place, trailed well behind at 12 percent. Energy prices was third at 8 percent.

The faltering economy had been expected to be a weakness for McCain, an Arizona senator and former Vietnam prisoner of war who has admitted a lack of economic expertise.

McCain has portrayed Obama, an Illinois senator, as a proponent of higher taxes, while Obama has tried to link McCain with President George W. Bush’s unpopular economic policies.

McCain backs an extension of Bush’s tax cuts, which are geared toward higher wage earners. Obama supports tax cuts for low- and middle-income earners and calls for higher taxes on those making more than $250,000 a year.

MCCAIN BACKS LIFTING OIL DRILLING BAN

In the face of surging gas prices, McCain has proposed lifting the ban on offshore oil drilling as a bridge to a new energy policy. Obama sharply criticized the plan and said it would provide no real relief.

“On balance, McCain probably scored on oil drilling because he looked like a man of action,” Zogby said.

The polling was conducted Wednesday through Sunday, mostly after a public flap over comments by former Texas Sen. Phil Gramm, a top economic adviser to McCain.

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Gramm said the United States had become “a nation of whiners” who are in a mental recession. McCain quickly distanced himself from the remarks, which Obama said showed how out of touch McCain was on the economy.

When independent candidate Ralph Nader and Libertarian Party candidate Bob Barr, who are both in the process of trying to add their names to state ballots, are included in the survey Obama’s margin over McCain grows to 10 percentage points, 46 percent to 36 percent.

Nader and Barr each picked up 3 percent, but nearly all of their support came from McCain. With Nader and Barr included, about 60 percent of conservatives back McCain, and 71 percent of self-identified Republicans support him.

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McCain has struggled at times to solidify his support among conservative Republicans, and has moved to mend fences on issues like immigration and taxes where he has bucked the party in the past.

Obama, an Iraq war opponent who has been labeled a liberal by Republicans, earned the support of more than one-fifth of voters who identified themselves as conservative.

“It appears that at least some conservatives are still looking for alternatives to McCain,” Zogby said.

Obama led McCain among women, Hispanics, blacks, Catholics, young voters, suburban voters and union households. He pulled into a tie with McCain among men.

McCain led Obama among white voters, born-again Christians, middle-income voters and older voters.

The national survey of 1,039 likely voters had a margin of error of 3.1 percentage points.

(Editing by David Wiessler)