Mr. Obama’s rise has been built in part on the idea that he represents a break from the established identities that have defined many of the nation’s divisions. To many, he embodies a promise to bridge black and white, old and young, rich and poor  and Democrats, Republicans and independents.

Even so, Mr. Obama does not come to the campaign with a reputation as one of the most accommodating bridge-builders in the Senate. And while he promises a very different politics from Mrs. Clinton, their voting records in the Senate last year were not strikingly different.

A recent analysis of key votes by The National Journal concluded that Mr. Obama had the Senate’s most liberal voting record in 2007; Mrs. Clinton ranked 16th. But of the 267 measures on which both senators voted, the National Journal analysis found that they differed on only 10. One of their major differences came on an amendment that called for the designation of the Revolutionary Guards in Iran as a terrorist organization; while Mrs. Clinton supported it, Mr. Obama missed the vote, but said he opposed it.

Congressional Quarterly said Mr. Obama voted with his party 97 percent of the time on party-line votes last year; Mrs. Clinton did so 98 percent of the time.

But it is Mr. Obama who is running on a promise of a new approach to politics. Given that, he says he understands the criticism of his voting record, but argues that the Senate is so ideologically polarized it is hard not to end up on one side or the other.

“The only votes that come up are votes that are purposely designed to divide people,” he said. “It’s true that if I’m presented with a series of votes like that, I’m more likely to fall left of center than right of center. But as president, I would be setting the terms of debate.”

Mr. Obama seems to be promising less a split-the-difference centrism than an ability to harness the support of all those voters who yearn for something new, beyond the ideological stalemate. In his book “The Audacity of Hope,” he wrote, “They are out there, waiting for Republicans and Democrats to catch up with them.”