* Obama campaign contemplates adjustments after debate defeat
* Democrat says didn't face 'real Mitt Romney'
* Reuters/Ipsos post-debate poll shows Romney boost
* 67.2 million saw debate
* Romney disavows "47 percent" remarks
By Jeff Mason
DENVER, Oct 4 (Reuters) - A day after a muted performance in a presidential debate, U.S. President Barack Obama fought back against Republican rival Mitt Romney on Thursday and the Democrat's re-election campaign vowed to learn lessons from the setback.
A feisty Obama told a rally of some 12,000 people that the former Massachusetts governor was untruthful during Wednesday's 90-minute debate in Denver, which most observers reckoned the Republican won.
"When I got onto the stage, I met this very spirited fellow who claimed to be Mitt Romney," Obama said.
"But it couldn't have been Mitt Romney, because the real Mitt Romney has been running around the country for the last year promising $5 trillion in tax cuts that favor the wealthy. The fellow on stage last night said he didn't know anything about that."
Often criticized for being wooden, Romney's aggressive debate performance gave his campaign a burst of energy after weeks of setbacks.
Looking at times tired and displeased, Obama did not seize opportunities to attack the Republican on his business record at Bain Capital, the "47 percent" video and his refusal to release more income tax returns.
And Romney tried to take the "47 percent" issue away from subsequent debates. In a damaging video from a private fund-raising speech, Romney had said in May that 47 percent of voters are dependent on government and unlikely to support him.
Three weeks after the video came to light, Romney completely disavowed the remarks for the fist time, telling Fox News what he said was "just completely wrong."
"Clearly, in a campaign with hundreds, if not thousands of speeches and question and answer sessions, now and then you're going to say something that doesn't come out right," he said.
The debate unfolded before a national television audience of 67.2 million, according to television ratings firm Nielsen, up 28 percent compared with the first presidential debate in 2008 between Obama and Republican Senator John McCain.
With two more presidential debates before the Nov. 6 election, senior aide David Axelrod said the Obama campaign would adjust its strategy as a result of the debate.
"We are going to take a hard look at this and we are going to have to make some adjustments as to where to draw the lines in these debates and how to use our time," he told reporters.
Democratic sources said Obama raised more than $100 million in September in another sign of his financial strength going into the last month of the campaign.
Romney prepared for the Denver encounter with days of mock debates and was more ready to go on the offensive against Obama in detailed discussion on taxes, jobs, energy and the budget deficit.
Obama is unlikely to add "huge amounts of additional prep time," for the two other debates on Oct. 16 in New York and on Oct. 22 in Florida, Axelrod said.
Part of the Obama strategy will be to attack Romney for what the Democratic campaign says are untruthful statements during the debate on his tax plan, Medicare and deficit cutting, as well as pressing him on what appeared to be changes in position on issues like bank regulation.
"We obviously are going to have to adjust for the fact of Mitt Romney's dishonesty," senior advisor David Plouffe said. "It's hard to remember a time in American politics when you have someone who is a major nominee for the presidency being that fundamentally dishonest about core parts of his campaign platform."
Obama spoke to a large crowd in Madison, Wisconsin, on Thursday afternoon that his campaign said was 30,000 strong.
ROMNEY SWAGGER, POLL BOOST
Romney had a bounce in his step and confidence in his voice as he addressed more than 10,000 supporters in Fishersville, Virginia, in the Shenandoah Valley.
In a sign of the importance of the state for him, Romney appeared together with his vice presidential nominee, Paul Ryan.
Romney, appearing after country singer Trace Adkins energized the crowd, said the debate offered two different visions for the country.
"What you didn't hear last night from the president is why it is the next four years are possibly going to be better than the last four years. He doesn't have a way to explain that, because he has the same policies for the next four years as he had for the last four years," Romney said.
The debate win was badly needed by Romney, whose poll numbers had dropped in recent weeks after several missteps and the release of a damaging video showed him disparaging 47 percent of the electorate as dependent on government aid.
Going into the debate, Obama held a lead of 5 to 6 percentage points over Romney in most national polls, and is ahead by at least narrow margins in almost all the battleground states where the election will be decided.
But Romney is now viewed positively by 51 percent of voters, the first time he has enjoyed a net positive in the presidential race, according to a Reuters/Ipsos poll taken after the debate. Obama's favorability rating remained unchanged at 56 percent.
Analysts said they still favored the Democratic president's re-election chances.
"Nobody is going to switch sides on the basis of this debate," said Samuel Popkin, a political science professor at the University of California at San Diego.
With the election little more than a month away, Romney might be running out of time to seize the lead. Voting has already begun in some form or another in 35 states, including in battlegrounds like Ohio and Iowa.
"For now, we'll chalk this up as a wake-up call for the president, who still has a vastly superior campaign organization and owns the pivotal issue of Medicare," Greg Valliere, chief political analyst at Potomac Research Group, said in a note to clients.
"But this is still a winnable election for Romney and that was the ultimate take-away last night," he said.
Obama faces another hurdle as soon as Friday morning, when the monthly jobs figures come out for September, a reminder of the tough economic plight faced by millions of Americans.
Economists polled by Reuters expect the unemployment rate to be anywhere between 8 and 8.3 percent, with non-farm payrolls adding 113,000 jobs, up from 96,000 in August.
In Europe, where leaders and finance officials have worked closely with the Obama administration to resolve the euro debt crisis, there was consternation at Romney's singling out of deficit-ridden Spain as a poorly administered economy.
"Romney is making analogies that aren't based on reality," Spanish Foreign Affairs Minister Jose Manuel Garcia-Margallo said after a meeting of his center-right party.
France's Le Monde was surprised by the sub-par performance of Obama, who wowed Europe with his 2008 election. "Where did the favorite go?" the newspaper asked on its front page.
Republicans who were worried that Romney's recent dip in polls might also drag down candidates for the House of Representatives and Senate at the election were relieved.
"Republicans everywhere have reason to be optimistic after last night's performance," said Senator Mike Lee, a favorite of Tea Party conservatives who have often been wary of Romney as too moderate.
Within hours of the debate, Republicans launched a string of ads hoping to capitalize on Romney's momentum. One had him presenting his plan for creating 12 million jobs. Another, aired in Wisconsin by the Super PAC, Restore Our Future, called on voters to demand better than Obama's "new normal" economy.
Romney's support of the coal industry during the debate sent coal company stocks up on Thursday. The Dow Jones coal index was 5.05 percent higher.
Shares of U.S. hospital operators fell as Romney's strong showing raised doubts about the future of Obama's 2010 healthcare reform.