We all remember those moments: President George H.W. Bush glancing at his watch in 1992; Vice President Richard Nixon’s sweaty face and loose shirt collar in 1960, Vice President Al Gore’s long sighs in 2000 and Texas Gov. Rick Perry in November 2011 trying in vain to remember what cabinet department he wanted to eliminate.

Those are just a few of the debate blunders etched in the public’s memory that both President Barack Obama and Republican presidential nominee Mitt Romney will try to avoid tonight in the first of three presidential debates that could decide one of the most contentious elections in American history.

“It only takes one mistake or one extraordinary comment before some important people re-evaluate the race,’’ said Nathan L. Gonzales, deputy editor of the non-partisan Rothenberg Political Report in Washington. “A majority of Americans don’t have to change their minds based on the debates. We’re talking a few swing voters in a few swing states.’’

Both candidates enter tonight’s debate with competing objectives. Obama will try to poke holes in Romney’s plans to overhaul Medicare and the tax code, while Romney has an opportunity to persuade undecided voters that he has a plan to ignite the nation’s sluggish economy.

“No matter how the campaign downplays it, it is a very important night for Mitt Romney and his campaign,’’ said Curt Steiner, a Republican consultant in Columbus. “There is a potential for a brand new ballgame at this stage and while the Romney campaign is down by a touchdown, there is still plenty of time left.’’

Dan Birdsong, a lecturer of political science at the University of Dayton, said that Obama’s “challenge is not to remind people, but solidify with people that what he’s been trying to do is the right course and that things are turning around, albeit slowly.’’

Unlike the Democratic and Republican conventions this year — which failed to generate massive TV audiences — the presidential debates tend to attract millions of viewers.

More than 63 million people watched the second debate in 2008 between Obama and Republican presidential nominee John McCain while 62.5 million watched the first debate in 2004 between President George W. Bush and Democratic presidential nominee John Kerry.

Yet even with huge audiences and the networks endlessly replaying in the following days any mistakes committed by the candidates, some are convinced that presidential debates are simply not that decisive in deciding the outcome of an election.

They point to Nixon’s dreadful appearance in the first of four debates with Democrat John F. Kennedy in 1960. Three physicians at the time told reporters Nixon looked as if he had suffered a coronary. Yet polls showed the race tight before the debates and Kennedy eventually prevailed by less than 120,000 votes in one of the closest elections in history.

In the 1980 debate in Cleveland, Republican Ronald Reagan’s dismissal of President Jimmy Carter – “There you go again’’ – was regarded as a moment of high drama. But even before that debate, polls showed that Reagan had crawled into a lead which he never relinquished.

In an interview last week in Ohio, Romney, the former governor of Massachusetts, said that “in the final analysis when we get past the impact of some extraordinarily inaccurate attack ads on (Obama’s) part and when we get a chance to actually talk about the real issues in the debates, then people will make an informed decision.”

Romney said he hopes to get the audience to focus on Obama’s record, saying that “these have been very difficult years for the people of this country and I think I can make peoples’ lives a good deal better. People understand that the president’s policies have not worked.’’

By contrast, Ben LaBolt, a spokesman for the Obama campaign, said that “we’ve heard Governor Romney has prepared some zingers. We will leave that to David Letterman. We don’t think that’s what the American people want.’’

Instead, LaBolt said that Obama’s “goal is to lay out the economic choice between building the economy from the inside out and not from the top down.’’ He said that viewers will be “looking for specifics from Governor Romney and he should explain how he will be paying for a $5 trillion tax cut for the wealthiest without raising taxes on the middle class.’’

But even as Romney and Obama say they will focus on issues, Birdsong of Dayton said that viewers “learn from the debates and it’s not just necessarily issue-based learning … What people learn in the course of debate is candidate characteristics or in some sense, character.’’

Joe Hallett of the Columbus Dispatch contributed to this story.