Obama goes through the night in quest for votes

Obama, locked in a neck-and-neck race with Republican Mitt Romney, pleaded with supporters Wednesday to cast early votes as he touched down in damp Iowa, chilly Colorado and took a helicopter through the gathering dusk in California.

Romney meanwhile, struggling to shrug off a new row over abortion and women's rights, fought back with a bold prediction that would win the November 6 election and consign Obama to the historical ignominy of a single term.

Obama's 40-hour, through-the-night trip will clock up more than 7,000 miles by the time he lands in Washington late Thursday, and is a signal of commitment and confidence that he can score right across the vast electoral map.

He opened Wednesday in the state where he made his name way back in 2008 -- Iowa -- telling voters that they knew they could trust him, but could not be sure exactly what Romney stood for, after a string of policy reversals.

Steering his "campaign marathon extravaganza" into Colorado, where he is locked in a close battle with Romney, Obama struck the theme of trust again, telling a 16,000 strong crowd: "You know I mean what I say."

Then Obama hopped into friendly Democratic territory in California, taping an appearance on "The Tonight Show With Jay Leno" and taking a humorous jab at old foe Donald Trump, who revived the conspiracy theory over his birthplace.

"This all dates back to when we were growing up together in Kenya," joked Obama, who was born in Hawaii to a Kenyan father and a white American mother.

"When we finally moved to America, I thought it would be over," the president said with a beaming grin, though he admitted that, in reality, he had never met the flamboyant property mogul.

Trump earlier offered to pay $5 million to a charity of Obama's choice if the president released his college records and passport applications, as he continued to press his case that Obama's past hides embarrassing secrets.

Obama later flew into gamblers' paradise Las Vegas for a late night rally -- under a huge sign reading "Vote Early" -- as his campaign tried to drive supporters to the polls to build up an unassailable edge on Romney in Nevada.

"We are pulling an all-nighter, and if you are not going to sleep you might as well be in Vegas," Obama said.

Air Force One was then set for a "red-eye" flight east through the night for an early morning rally in the largest swing state, Florida.

Romney was also on the trail in the battleground states Wednesday, appearing in Reno, Nevada, and Iowa, again seeking to build an impression that his recent polling surge can be sustained in the final days of the campaign.

"The Obama campaign is slipping because it can't find an agenda to help the American families," Romney said.

"I'm optimistic. I'm optimistic, not just about winning... we are going to win by the way..." Romney said.

But Romney again saw his hopes of leveling a devastating attack on the president's economic record frustrated by another row over the Republican Party's attitude to women's health issues and abortion.

Republican Senate candidate Richard Mourdock said that pregnancy caused by rape was "something God intended to happen" offering an opening for the Obama campaign, which said Romney backs 1950s style social policies.

"I don't know how these guys come up with these ideas... rape is rape. It is a crime," Obama told Leno, and warned that politicians had no business making decisions for women about their bodies and health choices.

The row put Romney in an awkward spot with women voters, who already back Obama in larger numbers and whose support could prove decisive in knife-edge state races on November 6.

But Romney is also wary of alienating evangelical voters and social conservatives, who oppose abortion as an article of faith and who form an important part of his base in battlegrounds like Ohio.

Many experts believe that Ohio could decide the race, and a survey by Time magazine released Wednesday put the president up by five points in the state.

There were also signs that Romney's momentum of the last few weeks was abating. The Republican led a RealClearPolitics average of national polls by just 0.6 percent.

On Thursday, Obama will go from Florida to Virginia, a traditionally Republican state which he won in 2008, and then head to Illinois to cast his own early vote, before ending his tour with an evening rally in Ohio.

Romney meanwhile was putting his sole focus on Ohio, with a bus tour across the state to include three rallies.