Barack Obama leads in four states won by President Bush in 2004 and is essentially tied in two other Republican states, according to new AP-GfK battleground polling that suggests most roads to victory are closed to John McCain. Obama could win big.

While no poll can predict next week’s results, the AP-GfK surveys explain why Obama is hoping not just for a win but a transcendent victory that remakes the nation’s political map. McCain is scrambling to defend states where he wouldn’t even be campaigning if the race were closer.

Less than a week before Election Day, the AP-GfK polls show Obama winning among early voters, favored on almost every issue, benefiting from the country’s sour mood and widely viewed as the winning candidate by voters in eight crucial states Colorado, Florida, Nevada, New Hampshire, North Carolina, Ohio, Pennsylvania and Virginia.

“I’ve never seen the United States in this bad of shape,” said Debby Granik, an executive assistant from Las Vegas who voted for Obama last week. “We need change. We need change desperately.”

Despite a mounting chorus of Republicans predicting their nominee’s demise, McCain aides insist their internal surveys show victory is still within reach.

Indeed, polls are mere snapshots of highly fluid campaigns, and this race has been unusually volatile. McCain was written off prematurely last year, and Obama seemed poised for victory in New Hampshire’s Democratic primary just before Hillary Rodham Clinton thumped him.

Even this close to Election Day, racial tensions and the numbers of late-deciding voters identified by the AP-GfK polling leave room for doubt. But the surveys confirm what McCain aides acknowledge privately their chances of winning are low.

The polling shows Obama leading in Ohio (7 percentage points), Nevada (12 points), Colorado (9) and Virginia (7), all red states won by Bush that collectively offer 47 electoral votes. Sweeping those four or putting together the right combination of two or three would almost certainly make Obama president.

It takes 270 electoral votes to win the White House. Obama can earn 252 by merely reclaiming states won by John Kerry in 2004. There are only two Kerry states still in contention Pennsylvania with 21 votes and New Hampshire with four and AP-GfK polls show Obama leading both by double digits.

Ohio alone has 20 electoral votes. Nevada has 5, Colorado 9 and Virginia 13.

In addition, Obama is tied with McCain in North Carolina and Florida, according to the AP-GfK polling, two vote-rich states Bush carried in 2004. Obama is throwing his time and money into the Sunshine State, which has 27 votes, part of a strategy to create many routes to victory and push toward a landslide of 300 or more electoral votes. North Carolina has 15 votes.

Independent polling suggests that New Mexico and Iowa, two traditionally GOP states, are out of reach for McCain. Other red states may be creeping away from him and into contention, including Montana.

The bottom line: McCain must overtake Obama in the many red states where he is trailing or tied a tall order. Or he needs to gain some breathing room by winning Pennsylvania, where he trails by 12 percentage points, according to the AP-GfK poll.

Many of his own supporters say the race is all but over.

“If you believe in miracles,” said GOP consultant Joe Gaylord of Arlington, Va., “you still believe in McCain.”

“I get the sense it’s shutting down,” said Tom Rath, a GOP consultant in New Hampshire where McCain trails by 18 points.

He added, “Where there’s a week, there’s hope.”

A couple of factors might cut McCain’s way.

First, there are still a good number of voters are open to changing their minds from as low as 4 percent in Nevada to 14 percent in New Hampshire.

Thomas Aelker, a Republican from central Florida who considered voting for Obama, said he’s back with McCain. He said of Obama, “I just think his lack of experience will be a detriment.”

Second, the impact of race is a hard-to-measure factor as Obama seeks to become the nation’s first black president.

In three states North Carolina, Florida and Pennsylvania the number of white Democrats who said the word “violent” described most blacks hit double digits in the polling.

In those same states, Obama was having trouble winning over white Democrats 20 percent of them in North Carolina said they were voting for McCain; 12 percent in Florida and 8 percent in Pennsylvania.

Obama may have coattails. Democrats lead the Senate races in Colorado, New Hampshire and Virginia, according to AP-GfK polls. In North Carolina, GOP Sen. Elizabeth Dole is essentially tied with state Sen. Kay Hagan.

In all four of those Senate races, the Democratic candidate leads among early voters, a sign of a strong ground game driven by the top of the ticket. Obama easily outpaces McCain among early voters, holding about a 2-1 advantage in six of the states.

Obama is favored on almost every issue in every state, the polling says:

Voters in all eight states gave him the highest marks on whom they trust to fix the economy and improve health care.

Even on the question of “who would make the right decision about national security,” typically a strong suit for McCain, Obama holds a slight lead in Nevada and is running even against his GOP rival in Colorado, New Hampshire, Pennsylvania and Virginia.

Obama’s message of change is playing well among women, especially in Florida where they gave Obama 54 percent of their support in the polling.

Susan Pogue, 56, of West Palm Beach, said McCain lost her vote during the final debate. “When it comes to meeting with world leaders,” she said, “I want someone who is not clucking and rolling his eyes.”

By large margins, voters in each of the eight states consider Obama the likely winner Tuesday.

Voters in each state believe McCain has run a far more negative campaign.

Seven in 10 Hispanics in Colorado say they are voting for Obama, a margin that could help him win a state that has chosen Democratic presidential candidates just three times since 1948.

The political landscape tilts against McCain. Just 8 percent of voters in New Hampshire think the country is headed in the right direction. Three-quarters of voters in Pennsylvania disapprove of Bush’s job performance. Nine in 10 voters in North Carolina are worried about the economy.

“I’m a Bush-generated Democrat,” said Connie Lilly of Richmond, Va.

The AP-GfK Battleground State Poll was conducted from Oct. 22-26 in eight states. It involved interviews by landline telephone with likely voters in each state, ranging from 600 in Florida and New Hampshire to 628 in Nevada. The margin of sampling error was plus or minus 3.9 percentage points in Colorado and Nevada, and 4 points in the other states.