"I think these battleground states have now closed up, almost all of them, and I believe there's a good scenario where we can win," McCain told CBS' "The Early Show" in an interview broadcast as the day's first voters stood in early-morning lines.
"Look, I know I'm still the underdog, I understand that," the Arizona senator said. "You can't imagine, you can't imagine the excitement of an individual to be this close to the most important position in the world, and I'll enjoy it, enjoy it. I'll never forget it as long as I live."
Obama campaign manager David Plouffe said he was confident that new voters and young voters would fuel an enormous turnout to benefit the Illinois senator.
"We just want to make sure people turn out," Plouffe told "Today" on NBC. "We think we have enough votes around the country."
Standing in line in one of the battleground states, Ahmed Bowling of Alexandria, Va., said the election "will mark a significant change in the lives of all Americans, and so we do have to come out as early as possible to cast our votes."
In Brooklyn, N.Y., 49-year-old Venus Kevin said the line at her precinct was "already down the block and around the corner" when she arrived shortly before 6 a.m. EST.
"Obama is the man," said Kevin, who is black. "His message and his vision has reached a lot of people, not just African-Americans."
The contest pitted the 47-year-old Obama, a first-term Illinois senator who rocketed to stardom on the power of his oratory and a call for change, against the 72-year-old McCain, a 26-year lawmaker whose mettle was tested during 5 1/2 years as a prisoner of war in Vietnam.
"I'm feeling kind of fired up. I'm feeling like I'm ready to go," Obama told nearly 100,000 people gathered for his final rally Monday night in Virginia.
"At this defining moment in history, Virginia, you can give this country the change it needs," Obama said to voters in a state that hasn't voted for a Democratic presidential nominee in 44 years.
The Illinois senator's final day of campaigning was bittersweet: He was mourning the loss of his grandmother, Madelyn Dunham, who helped raise him. She died of cancer Sunday night, never to see the results of the historic election.
McCain completed a cross-country trek through seven battleground states before arriving at home in Phoenix early Tuesday morning.
"This momentum, this enthusiasm convinces me we're going to win tomorrow," McCain told a raucous evening rally in Henderson, Nev. It was the fifth campaign stop in an 18-hour odyssey that took him across three time zones.
Obama planned a quick campaign stop in Indiana on Election Day before a massive outdoor rally in front of the skyline in his adopted hometown of Chicago. The day's forecast was for an unseasonably warm 70 degrees.
McCain planned events in Colorado and New Mexico, then a party at the Biltmore Hotel in Phoenix.
Obama urged his supporters to resist overconfidence. "Even if it rains tomorrow, you can't let that stop you. You've got to wait in line. You've got to vote," he said.