Their optimism, which is said to be shared by the Democratic candidate himself, is based on information from private polling and on faith in the powerful political organisation he has built in the key swing states.
Insiders say that Mr Obama’s apparent calm through an unusually turbulent election season is because he believes that his strength among first time voters in several key states has been underestimated, both by the media and by the Republican Party.
Mr Obama has come under fire from within Democratic ranks over his message and his tactics. Critics say he has failed to connect with the blue-collar workers seen as crucial to winning the election, and too reluctant to make direct attacks on Mr McCain.
But his aides are convinced that he has a strong chance of winning no fewer than nine states won by George W.Bush in the closely contested 2000 election, including former Republican strongholds like North Carolina, Virginia and even Indiana, which have not voted Democrat for a generation.
David Axelrod, Obama’s chief strategist, said last week that Obama had "a lot of opportunity" in states which Mr Bush won four years ago.
But in private briefings in Washington, a member of Mr Obama’s inner circle of policy advisers went much further in spelling out why the campaign’s working assumptions far exceed the expectations of independent observers.
"Public polling companies and the media have underestimated the scale of new Democratic voters registration in these states," the campaign official told a friend. "We’re much stronger on the ground in Virginia and North Carolina than people realise. If we get out the vote this may not be close at all."
To win the presidency, Mr Obama must win 270 votes in the Electoral College, which awards votes to the winner of each state broadly in proportion to the size of the population.
Statewide surveys put the likely Electoral College result at a slender Obama win, 273-265. But his campaign staff believe they have a good chance of securing between 330 and 340 votes, and could win up to 364 votes, a landslide on the scale of Bill Clinton’s wins.
The senior Obama advisor said that the Democratic nominee is confident of winning all the states held by John Kerry, the Democratic candidate four years ago, a total of 252 votes.
But his team believes he can also bank victories in Iowa, where he first emerged as a force in the campaign in January, and New Mexico, where Mr Kerry only lost by 20,000 votes in 2004. Those states would leave him just six votes short of outright victory.
Taking Colorado, as Mr Obama’s team are very confident of doing, would put him over the top. Even winning the smaller state of Nevada, with its five electoral votes, would be enough to guarantee a 269-269 tie with Mr McCain. If that happens, the US consititution would hand the decision over to the Democrat dominated US House of Representatives, which would presumably come down in Mr Obama’s favour.
Most pollsters would regard those expectations as uncontroversial. But the Obama camp is also confident of winning Ohio and Virginia, which commentators believe are "toss up" states with the two candidates chances at 50/50.
Last week Mr Obama began investing heavily in advertising in Indiana, Florida and North Carolina, which many had supposed to be a waste of time and money.
A Washington official who has discussed the electoral mathematics with one of Mr Obama’s senior advisers told reporters that the campaign is spending money only in states which it believes can, and indeed ought to, be won.
"Obama has many more paths to the nomination than McCain," the source said. "They think they can defend the Kerry states. Iowa is gone. That’s five votes. New Mexico is in the bag. Then Obama has four or five different ways of winning. He can go Nevada or Colorado, Virginia, any of those, even Indiana.
"McCain has got to run the board, the whole Bush table. He can probably lose New Mexico and Iowa. He can’t afford to lose anything else."
The official added: "The poll numbers say Florida’s back in play. McCain hasn’t spent a single penny there and that’s Obama’s calculation, that he can capitalise on that. The Republicans can’t lose Florida or they’re done for."
Conventional wisdom among pollsters is that Mr Obama is at risk of losing both Michigan and Pennsylvania and possibly even Wisconsin, all large Kerry states whose loss would be a damaging blow.
But the Obama camp believes that Wisconsin in safe and that he has strengthened his position in Pennsylvania with a good ground operation. Michigan, home of the Reagan Democrats, is a concern because Mr Obama did not campaign there in the primaries and race relations are raw, but they are confident they can hang on to his slender lead in the polls.
Mainstream pollsters on both sides of the aisle last week called the election as a dead heat. Mark Mellman, who was John Kerry’s polling guru, said the 2008 election is "increasingly resembling the real map of 2004" and Matthew Dowd, a top strategist on Bush’s re-election campaign, added: "States that were reliably red are reliably red, and states that were reliably blue are reliably blue."
But Mr Obama’s campaign team reject that analysis. Their confidence that good organisation will more than compensate for latent racism will be reassuring to some Democrats, who were concerned by a poll last weekend that found Mr Obama would be six points higher in the polls if he were white.
The scale of their ambition will trouble those Democratic sceptics who consider Mr Obama’s aides to be complacent and inexperienced in national campaigns.