For Mitt Romney, these last two weeks have been a brutal stretch.

He’s fallen behind in critical battleground states, polls show. Furor over a video of Romney declaring 47 percent of Americans “dependent on government” and “victims” eclipsed his message for days. Panicked Republicans tell him to turn it around fast — or lose on Nov. 6.

On Wednesday, Romney gets what could be his best chance to change the trajectory of the 2012 election when he steps on the stage in Denver to debate President Barack Obama.

“Romney can use the debate to hit ‘reboot’ and get the focus back on the economy and the failings of the incumbent,” said Christopher Nicholas, a Pennsylvania Republican strategist. “He will be able to force Obama to talk about what he’s been able to avoid for the last couple of weeks: the unemployment rate.”

It is the first of three nationally televised debates that will dominate the last month of the campaign. If 2008 is a reliable indicator, they could reach audiences of up to 60 million Americans — by far the largest of the campaign.

Recent polls show Obama with growing leads in Ohio, Florida and Virginia, perhaps the three most important of the dwindling number of swing states.

History suggests Romney will benefit from the elevating effect that challengers get from being on an equal footing with the incumbent: same stage, same bland lecterns, same lighting.

His advisers have signaled that Romney will be aggressive in attacking Obama’s economic record, hoping to put the President on the defensive and provoke him into making a mistake. In some polls, though, voters now rate Obama better on the economy than the former business executive.

Presidential debate lore is long and rich, with ready examples of blunders and moments that are considered pivotal: a haggard Richard Nixon next to the vigorous JFK in 1960; George H.W. Bush glancing at his watch during a town-hall debate in 1992; Ronald Reagan in 1984 answering a question about his advanced age by saying he would not make an issue of Walter Mondale’s “youth and inexperience”; Al Gore sighing in 2000.

Yet political scientists who have sifted through the available polling evidence have found debates have rarely, if ever, shifted enough votes to decide a presidential election by themselves.

“While it’s true that debates aren’t usually game changers, the possibility exists,” said Mitchell McKinney, an associate professor at the University of Missouri who specializes in political communication. “There’s always an opportunity. That’s why we’ll watch.”

At most, writes political scientist John Sides of George Washington University, “debates may provide a ‘nudge’ in very close elections like 1960, 1980 or 2000.”

Because debates are not the only things voters are seeing and hearing before the election, it is hard to isolate them as the cause of any shift in voters’ preferences.

Even so, after Gore’s widely mocked interruptions of George W. Bush, sighing audibly and rolling his eyes in the first 2000 debate, there was a swing of 2 or 3 points in the polling toward Bush, enough to give him a narrow lead. Political scientists Robert Erikson and Christopher Wlezien concluded that after all the debates, Gore’s standing was 2 percentage points lower than it had been beforehand.

Studies have also shown debates tend to reinforce the partisan leanings of those watching, but that doesn’t mean they are not influential with undecided voters, said political scientist Marjorie Hershey of Indiana University. News coverage and discussion of the events can be persuasive, she said.

“A lot of people will get their information from ‘soft-news’ sources _ they will hear about the debate in Jay Leno’s monologue or on Jon Stewart,” Hershey said. “They will listen to a discussion on ‘The View.’”

This year, polling has found a smaller pool of undecided voters than in other recent elections.

The campaigns are preparing for a make-or-break night on Wednesday.

Since Romney cleared the primaries, his staff has blocked off time for the former Massachusetts governor to study for the debates almost daily.

During the Democratic convention this month, Romney even hunkered down for debate dry-runs at a remote Vermont resort.

Obama has also had some preparation sessions and was scheduled to huddle with his advisers this weekend in Nevada to practice.

Two more national unemployment reports are due before Nov. 6, and the world, as shown by the latest violence in the Mideast, is volatile. Nobody could have predicted the Obama administration’s shifting explanations for the deadly attack on the U.S. consulate in Benghazi, Libya; the assault now appears to have been a coordinated attack by terrorists, providing grist for Romney’s criticisms of the President’s foreign policy in the region.

The challenger can’t count on external events, however.

(Romney will be up against “one of the most talented political communicators in modern history,” senior adviser Beth Myers wrote in a campaign memo.

And in a way, Romney’s recent difficulties could work to his advantage.

“It’s much easier for Romney to do well because of the story line in the mainstream media over the last two or three weeks,” Hershey said. “He’s had a horrible time. Comedians are making fun of him. … Basically, all he has to do is remain coherent. The story line is ripe for change.”

GOP strategists point out that Obama can come across as arrogant and professorial; during a debate before the 2008 New Hampshire primary, he told Hillary Clinton she was “likable enough,” an aside that sounded condescending to many listeners.

“Obama’s got to watch out for hubris and being flippant,” Nicholas said. “Until now, he’s never been on the same stage with Romney, and it’s a different dynamic when you’re six feet away from each other.”