His image as a centrist took hold at the 2004 Democratic National Convention, where he gave a speech hailing not the blue states or the red states but the United States of America.
But over the course of Obama's first term, this analysis increasingly sounded like wishful thinking. And never more than during the past week, with the nomination of Chuck Hagel to be secretary of defense and with Speaker John Boehner's revelation that in his negotiations last month Obama repeatedly insisted that "we don't have a spending problem."
Obama went ahead with the Hagel nomination even though Hagel has been greeted with sharp criticism from many of his fellow Republicans and with eloquent silence by elected Democrats.
It's not difficult to understand why. On foreign policy and defense issues, Hagel stands not somewhere between the two parties but conspicuously to the left not only of Republicans but of most Democrats -- and to the left of many of the president's own policies.
For example, Hagel was one of two Republican senators who in 2007 voted against designating Iran's Islamic Revolutionary Guards as a terrorist organization. The Obama administration accepts that designation.
Hagel has consistently voted against and opposed sanctions on Iran. Obama ran for re-election touting the increased sanctions he has adopted at the insistence of bipartisan congressional majorities.
Hagel has said that military action against Iran is "not a viable, feasible, responsible option." Obama has insisted that all options are on the table should negotiations and sanctions fail to deter Iran from obtaining nuclear weapons. Hagel has supported direct negotiations with the terrorist group Hamas. Obama has not.
Obama's Defense Secretary Leon Panetta has said that the defense cuts that would be imposed by sequestration would be "devastating." Hagel in a September 2011 interview called the Defense Department "bloated" and added, "I think the Pentagon needs to be pared down."
Hagel has shown an animus against Israel that is in tension with Obama's assurances that Israel is a valued ally. He was one of only four senators who refused to sign a letter urging the president to express solidarity with Israel and condemn the Palestinian campaign of violence.
In an interview with Middle East negotiations veteran Aaron David Miller in 2006, Hagel said, "The Jewish lobby intimidates a lot of people," and, "I'm not an Israeli senator, I'm a United States senator."
But American support for Israel is not the product of a sinister "Jewish lobby." It's a reflection of the strong pro-Israel beliefs of the vast majority of Americans.
Confirmation of Hagel will be taken by the Iranian regime as an indication that the United States will do nothing to stop it from obtaining the nuclear capacity that Israel understandably regards as a threat to its existence.
So it's not surprising that the Washington Post editorial page, which supported Obama's re-election, stated that Hagel "is not the right choice for defense secretary."
Obama's decision to nominate him anyway suggests a leftward lurch on policy for which voters were given no advance notice.
It's not surprising that most Republican senators seem likely to vote against this Republican nominee -- and that most Democratic senators are avoiding making any commitment. Even the voluble Chuck Schumer is keeping quiet.
Democrats are keeping quiet too about Obama's insistence that "we don't have a spending problem." For three years, Senate Democrats have refused to pass a budget resolution while government spending as a percentage of gross domestic product continues at the highest level -- 24 to 25 percent -- since World War II.
Obama was unable or unwilling to negotiate a grand bargain with Boehner in the summer of 2011 and again last month, and insists he won't cut spending in return for an increase in the debt ceiling next month.
"I'm getting tired of hearing you say that," he responded in irritation at Boehner's insistence on doing something about spending. So the dealmaking to avoid the fiscal cliff was left to Vice President Joe Biden and Senate Minority Leader Mitch McConnell.
Obama has sometimes talked of reforming entitlement programs. But his unwillingness to address spending looks like another unannounced lurch to the left.