Former Canadian Liberal leader Michael Ignatieff calls it "a strong definition of what a progressive politics ought to stand for," in the U.S. and elsewhere.
The Washington Post reports that Obama used his address "to make the case for a liberal last-term agenda." James Fallows, national correspondent for The Atlantic magazine, who worked as president Jimmy Carter's chief speechwriter, calls it "the most sustainedly 'progressive' statement Barack Obama has made in his decade on the national stage."
Politico.com, a much-followed website in Washington, headlines it "Return of the liberal," while in Israel, a headline in the left-leaning daily Haaretz says "Obama presents a 'progressive manifesto.'"
The speech is especially noteworthy for being the first inaugural address to discuss gay rights and climate change, and for how Obama framed his agenda in the context of the principles of his country's founders.
Obama's liberal agenda
Ignatieff, who now teaches at the Kennedy School of Government at Harvard University, says this was "a strongly defined agenda, for not only liberalism and progressive politics in general but for his second term."
He considers the climate change reference a "very important signal rhetorically and I just hope it's followed up with action."
Ignatieff told CBC News that Obama gave a "classical liberal speech," even when using lines like, "We have never relinquished our skepticism of central authority, nor have we succumbed to the fiction that all society's ills can be cured through government alone."
Ignatieff considers those themes authentically liberal. "If you are going to advance a social justice agenda and a climate change agenda, you have to be very clear about what government can and cannot do," he argues. "This is not big government liberalism, this is austerity liberalism."
The former Liberal leader, echoing Obama, notes that "government is not always the solution, it can sometimes be the problem."
Emphasis on peace
On foreign policy, Ignatieff notes that Obama "put enormous emphasis on peace rather than war," adding that "it's very clear he wants to have American soldiers out of combat everywhere" by the time he leaves office in four years.
The former Liberal leader, in Cambridge, Mass., where he watched Obama on television, was struck by how the president didn't lift the crowd. "That bonding between speaker and audience just wasn't there," Ignatieff, who has given many a speech over the years, observes.
He thinks that Americans trust and like Obama but argues, "they're not excited by him and he may need excitement to get some of these things done."
Four years ago in Washington, the enthusiasm for Obama's first inaugural was strong while his speech was short on specifics. This time, "he's very specific about what he wants to achieve but there's much less enthusiasm from the watching crowd, at least on the mall in Washington."
Speechwriter Mary Kate Cary says an inaugural address is supposed to motivate your audience to get off the couch and take action, but she feels Obama's speech failed to achieve that goal.
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Cary, who was a speechwriter for president George H. W. Bush from 1988 until 1992, says Obama would have come closer to that goal had he "done a lot more setting up the issues he talked about in terms of our children and grandchildren, and that would have been very well received." She observes that Obama got some of the biggest applause when he said, "We will respond to the threat of climate change, knowing that the failure to do so would betray our children and future generations," but not for what followed on that issue.
She considers the speech more like one for a Democratic Party convention or the State of the Union because it was more programmatic than past inaugural speeches. "Inaugurals are more vision statement, the state of the union more follow-up of how to accomplish that vision through specific programs."
Framed in the values of the founders
Cary told CBC News she was impressed by how Obama framed just about every "liberal cause" that he talked about "in terms of the founders and the constitution," which she says is "an olive branch to the other side, especially the tea partiers."
"Setting up the gay rights argument as the founder's notion of equality, that all are created equal, is the argument to use if you're trying to persuade social conservatives." She explains that she's "a conservative and for gay rights for that reason."
Obama's also got one of the biggest rounds of applause from the crowd on the Washington Mall when he said, "Our journey is not complete until our gay brothers and sisters are treated like anyone else under the law, for if we are truly created equal, then surely the love we commit to one another must be equal as well."
American author Robert Caro, famous for his multi-volume biography of president Lyndon Johnson, said before Obama's second inauguration, that "when you have a second term, there's nothing left to run for except your place in history," so in the speech, "you are setting out what you want to do."
An hour after his speech, Obama emailed his supporters in the grass roots movement Organizing for Action, that, "Now it's time to finish what we started — let's get going."