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In a hastily called meeting Monday afternoon, Mr. Obama huddled with unhappy House Democrats at the White House as the tax-cut negotiations continued.

But even before the meeting, Rep. Anthony Weiner, New York Democrat and one of Capitol Hill’s more outspoken liberals, said Mr. Obama was unable to see “the value of being on offense.”

Middle-class Americans, Mr. Weiner said, “see [the deal] as punting on third down.”

At the North Carolina community college, Mr. Obama made an explicit defense of the need for more public spending in at least some strategic areas.

“The hard truth is this: In the race for the future, America is in danger of falling behind,” he said.

The president urged congressional lawmakers to put aside short-term political wrangling. “There should not be any inherent ideological differences to making our economy more competitive.”

Recalling that the 1957 launch of the Soviet satellite served as a “wake-up call” for Americans, the president told the crowd of students, professors and guests at Forsyth Technical Community College that responding to a modern-day “Sputnik moment” will require investment.

But breaking the political impasse over taxes proved to be difficult, and threatened to hold up other Democratic priorities for the brief lame-duck session.

Even as Senate Democrats failed to overcome a Republican filibuster on the issue over the weekend in a rare Saturday session, many of the president’s political allies were urging him to take a hard line on the tax cuts.

Earlier Monday, after touring the Winston-Salem, N.C., community college, the president gave an upbeat speech loaded with patriotic references to Abraham Lincoln, John F. Kennedy and critical national accomplishments such as the Transcontinental Railroad, framing the spending battle in Washington as a pivotal moment in American history.

“The most important contest we face is not between Democrats and Republicans; it’s between America and our economic competitors around the world,” Mr. Obama said.