Gail Gitcho, communications director for the Republican Romney, said the campaign stands by the ad, which shows Obama speaking during the 2008 presidential race.
In the clip, Obama said, "If we keep talking about the economy, we are going to lose." The ad appears to be an admission that his stewardship of the economy is failing.
But Obama was actually quoting an adviser to then-Republican rival Sen. John McCain at the time.
The weak economic recovery from the 2008-2009 financial crisis and the stubborn 9 percent unemployment rate are so far the key issues heading into the 2012 race for the White House.
"We were upfront about the content of the ad - we sent out e-mails, cited the quote in our press release, talked to reporters about it, etc," Gitcho said in an e-mail. "We were very upfront. We included that portion intentionally."
The White House on Tuesday condemned the ad, accusing the Romney campaign of dishonesty.
While former U.S. House of Representatives Speaker Newt Gingrich has risen in recent national polls, Romney is among the front-runners to win the party's nomination to take on Obama.
Gitcho said that the Republican's campaign is "not backing down just because the Democrats don't like an ad from our campaign."
Republican strategist Kevin Madden, an adviser to the Romney campaign, noted that the ad had an approval disclaimer from Romney indicating the candidate approved of the language and quote used in the ad.
Madden said the ad is proof that Romney will go hard after Obama in the race for the White House in 2012.
"It's very important that Republican voters know the Romney campaign is going to take the fight to Obama and never give them even an inch," Madden said.
(Editing by Philip Barbara)