As the longest presidential campaign in memory careers through its final weekend, George W. Bush and Al Gore are running step for step across an electoral map filled with states too close to call.

Not in at least 20 years, and perhaps 40, has the result of a presidential race appeared so uncertain in the last hours before election day.

Polls give Bush a narrow advantage, but Al Gore is showing enough strength in key battleground states to keep alive the hope of a victory.

Adding to the uncertainty was the unpredictable impact of last week's revelation that Bush had been arrested for driving under the influence of alcohol in 1976, and might have misled a reporter who earlier asked him if he had ever been arrested after 1968, when he was charged with stealing a Christmas wreath, an event described as a fraternity prank.

Early polls from ABC found no impact from the story. Just one Bush supporter of 700 surveyed said the news caused him to shift his vote to Gore. But the race is so close some analysts feel its impact, if any, cannot be measured until election day.

In both parties, most experts see no signs that voters are poised to make the kind of decisive late break that, for instance, carried Ronald Reagan to a landslide victory over Jimmy Carter on the campaign's last weekend in 1980.

"There's a drift, as opposed to a trend, in our direction over the past week," said Tom Cole, chief-of-staff at the Republican National Committee. "I don't see anything as dramatic as 1980 . . . Something like that could occur but my sense is . . . it is going to go right to the end in a very close contest."

And that means both sides will spend the campaign's last hours scrambling for every possible advantage.

Which is why trade unionists were canvassing door to door on Saturday morning, Gore was barnstorming his home state of Tennessee, liberal groups in the Pacific north-west were frantically trying to push Ralph Nader supporters to Gore, and the National Rifle Association was firing endless volleys of phone calls into the battleground states for Bush.

Inspiring all this activity was a shared conviction encapsulated by Democratic pollster Celinda Lake: "If no outside events intervene, it will be toe to toe until the end, and turnout will be the thing that decides it."

National polls released on Saturday showed Bush holding strong but not pulling away. His lead in three surveys ranged from two to four percentage points.

What has made this contest so distinctive is not only the narrowness of the national margin, but the profusion of states in play on the campaign's last weekend.

With Bush displaying the capacity to contest Democratic-leaning areas, such as Iowa and Minnesota, and Gore confounding expectations by pressing Bush to the wall in Florida, the two sides were fighting this weekend for more than a dozen states at the tipping point.

Surveys released on Saturday night by independent pollster John Zogby showed Bush and Gore within two points of each other in Florida, Pennsylvania, Missouri, Tennessee and Wisconsin. Gore led by three in Washington State.

Indeed, so many states remain within reach of either man that even optimistic predictions on both sides have produced cliffhanger results.

One senior union official privy to Democratic polling this week estimated that Gore would win 273 electoral votes, just three more than the 270 needed for victory.

Likewise one assessment completed last week at the RNC gave Bush 287 electoral votes, and that total included Michigan, where almost all public polls last week showed Gore ahead. If Gore won Michigan's 18 electoral votes, and all the other states followed the RNC's projection, the two men would be tied at 269 electoral votes, throwing the race into the House of Representatives.

A tie, of course, remains a distant possibility. Still unlikely, but less remote, was the chance that Gore could narrowly lose the popular vote, yet eke out an electoral college majority.

That hasn't happened since 1888 when Grover Cleveland, a Democrat, won the popular vote but lost an electoral college majority to Republican Benjamin Harrison.

Some analysts think it can't be ruled out this year because Bush is rolling up huge margins in the south and mountain west, while public polls show Gore even or ahead in critical battlegrounds, such as Michigan, Pennsylvania, Florida, Wisconsin and Washington. Bush aides see little prospect of a split verdict because they say their private polling shows them leading in most of those states.

The most worrisome trend for Democrats was not only Bush's consistent lead in the national polls but the hints that Gore might face a ceiling in his support. Although Bush's lead over Gore in the national surveys has fluctuated over the past weeks, Gore has rarely polled above 45 per cent in any survey since the first presidential debate in early October.

Most pollsters believe that if an incumbent president (or senator or governor, for that matter) was polling only in the mid-40s so close to election day, he would be almost certain to lose, because most voters who are undecided at that late date tend to vote against the incumbent. But Gore isn't literally an incumbent, which makes the calculation more complex. "It's not a guarantee that the undecided break against him," Ms Lake said.

In nine of the past 13 elections, most voters who decided in the final two weeks have broken against the party holding the White House, according to University of Michigan surveys. But the history is more mixed on presidential elections without an incumbent running, as is the case this year.

In 1952 and 1960 the vast majority of late-deciders broke for the nominee of the party out of the White House, Republican Dwight D. Eisenhower and Democrat John F. Kennedy respectively. But in the open-seat presidential elections of 1968 and 1988, late deciders split almost evenly between the two major parties.

Given that history, Gore strategists privately acknowledge that they are unlikely to capture a majority of the remaining few voters who are undecided.

Instead, their hope is that many of those voters either stay home, or support one of the third-party candidates rather than Bush. There's precedent for that: Ross Perot ran extremely well among late deciders in both 1992 and 1996, the University of Michigan studies found.

Gore's advisers believe they have a better chance of overtaking Bush by recapturing some of the liberals now supporting Nader. But mostly they are hoping for a big turnout of Democratic base voters.

Republicans, who are working just as hard to turn out their base, remain cautiously optimistic that they can slightly increase the share of the votes cast by their partisans.

The two sides are battling for infinitesimal advantage, a change of a point or two in the share of the vote cast by union households or conservative Christians. "Unless the independents break decisively, they are not going to make the difference," Tom Cole of the RNC said in an assessment that top Democrats echo. "It is going to be who gets their people out. Honestly, we're not going to know that for 48 hours. It's just a great campaign."