WASHINGTON — As the White House race shows signs of tightening nationally, President Barack Obama’s campaign is banking on a massive get-out-the-vote operation and state-by-state shades of economic improvement to maintain its apparent polling edge in battlegrounds from Ohio to Virginia.

Republican Mitt Romney, re-energized by last week’s debate in Denver, is flashing new confidence on the campaign trail and pressing toward the political center on both foreign and domestic issues.

But his aides have outlined no clear path to winning the 270 Electoral College votes required to gain the White House.

“Things are going pretty good,” the usually cautious Romney said Monday with a smile.

Among Democrats, the swagger of the previous few weeks has all but vanished since the debate.

“Ultimately this is a tight race, and it’s going to remain a tight race until the end,” said Bill Burton, who runs Priorities USA Action, a pro-Obama super political action committee.

Indeed, one month from Election Day, polls show a close race. And with millions of Americans already voting and the potential for game-changing moments diminishing, the candidates have little room for error as they seek to sway a narrow swath of undecided voters.

Obama aides acknowledge Romney’s strong turn on the debate stage helped him shift gears from a rocky September. But they also argue that Romney’s momentum was arrested somewhat by a Friday jobs report showing the unemployment rate declined to 7.8 percent, the lowest level of Obama’s presidency.

They say the president was thrown during the debate by what they call Romney’s willingness to abandon his previous positions, including his $5 trillion tax cut proposal. In the next debate — and in television advertisements before then — the Democrat and his aides are expected to accuse Romney of lying about his own plans.

Romney’s team, meanwhile, is tempering expectations that tightening national polls will translate into success on the ground in the key states most likely to decide the race. Things may be moving in the right direction, they say, but significant work remains.

Still, they’re seeking to paint Obama’s campaign as desperate.

“It seems pretty clear that their new strategy is basically just call us liars, to descend down into a mud pit and hopefully, with enough mudslinging back and forth and distortion, people will get demoralized and they can win by default,” said Romney running mate Paul Ryan.

Both Democrats and Republicans say internal campaign surveys following last week’s debate show Romney has cut into the lead Obama had built up in many key battleground states. But they say Obama still has an advantage in most of the nine or so critical states, including Ohio and Virginia. A lack of independent polling makes it difficult to know whether that’s true. Romney pulled ahead of Obama, 49 to 45 percent nationally, among likely voters according to a Pew Research Center poll conducted after the debate.