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“That is kind of what he has talked about during the campaign, and he didn’t do it in a way that was offensive, I didn’t think so,” Mr. Sessions said. “He advocated what he believed in.”

But the lawmaker from Alabama chastised the president for his overall approach to governing by saying the Democrat “still advocates a larger, expansive government.”

“He believes that growth, prosperity, innovation, railroads are all done by the government, and I don’t,” he said.

Rep. Cathy McMorris Rodgers of Washington state, the chairwoman of the House Republican Conference, said the president’s “eloquent words must be matched with deliberate actions to restore country’s fiscal health” — suggesting a gulf between the two.

“In his inaugural address today, he said: ‘We must make the hard choices to reduce the cost of health care and the size of our deficit,’” she said. “Yet, it is almost four years since the [Democrat-controlled] Senate passed a budget. In the meantime, spending has raged out of control and America’s debt has ballooned.”

Mr. Obama’s second inauguration lacked the electric enthusiasm of his first, when an estimated 1.8 million people jammed onto the Mall to witness the swearing-in of the nation’s first black president. But Senate Majority Whip Richard J. Durbin, Illinois Democrat, said he was still plenty impressed with the crowd, which an inauguration official estimated to be at least 1 million.

“The people who were saying that there would not be so many people, I mean we looked all the way down the Mall — and it was packed. You know, all the way,” Mr. Durbin said. “This is a president who will never run for office again.”

David Axelrod, a former senior White House adviser to Mr. Obama and senior strategist for his 2012 re-election campaign, said it’s understandable that the president’s second inauguration didn’t stoke the same level of excitement as his first because “there is a difference when you are brand new.”

“I think the country likes this president. I think they support this president, and now he has four years to finish the work that he has begun,” Mr. Axelrod said.

“We are in a much different place than we were four years ago when we hurtling toward a second Great Depression. We have a foundation upon which to build.”

Seth McLaughlin contributed to this report.