When President Obama walked into the White House briefing room a little before 11 p.m. Wednesday, he had the air of a disappointed father who couldn’t get his kids to stop fighting.

House Speaker John Boehner (R) of Ohio, Senate majority leader Harry Reid (D) of Nevada, Mr. Obama, and Vice President Biden – and members of their respective staffs – had failed to break the budget impasse. The clock was ticking toward a government shutdown, which will begin at 12:01 Saturday morning if no deal is reached.

But even as Obama warned that a shutdown would have “real consequences for real people” – citing an example from the evening news of a man from Kentucky desperate for his tax refund – the president maintained his trademark measured tone. No chest-beating, no dire rhetoric. Classic Obama, yes. But also a recognition that this showdown over funding the federal government for the rest of the 2011 fiscal year is merely spring training for the big show ahead: the looming vote in Congress to raise the federal debt limit.

“Obama’s a guy who takes [presidential scholar] Richard Neustadt’s advice seriously: ‘Consider tomorrow,’ ” says Bruce Buchanan, a political scientist at the University of Texas at Austin.

And there are several layers of “tomorrow” at play as he navigates his new world of divided government. There’s the current impasse, which analysts seem to think should be resolved fairly quickly, if not by Saturday morning. Then there’s the debt ceiling, which Congress will have to raise in the next few months to prevent a government default.

Another dimension for Obama is political. “He needs to attract independents in the next election, and he knows that dire rhetoric doesn’t appeal to independents,” says Mr. Buchanan.

Still, some analysts find Obama’s approach curious, as he continues to travel and emphasize other issues, such as clean energy, even as the government approaches shutdown – an event that could sideline 800,000 federal workers and disrupt the fragile economic recovery.

“There’s an element of theater in this,” says Marc Landy, a political scientist at Boston College. “But Obama is the wizard of nonchalance. There’s something to be said for saying, ‘I’m going to give every nerve to this struggle, and if the Republicans don’t do likewise, it’s on them.’ ”

Peter Fenn, a Democratic strategist, leans more toward the “no sweat” side of things – and sees evidence of a learning curve in Obama’s performance after two years in office.

“He knew the odds were it would come down to the bitter end,” says Mr. Fenn. “Everyone’s been saying, ‘Where was he three weeks ago?’ The point is, we would still be right where we are now, regardless of what Obama did three weeks ago.”