One day after a muted performance in a presidential debate, President Barack Obama got tough on Republican rival Mitt Romney on Thursday as 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 Tuesday'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.

With two more presidential debates before the November 6 Election Day, 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.

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 squeeze in much more preparation for the two other debates, on October 16 in New York and on October 22 in Florida, Axelrod said.

"I don't see us adding huge amounts of additional prep time. I think there are some strategic adjustments that have to be made and we'll make them," he said.

Part of the Obama strategy will be to attack Romney for what it 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.

Romney had a slight swagger about him as he made a surprise visit to a meeting of conservatives in Colorado on Thursday morning. The crowd whooped and cheered as he was introduced.

"Last night I thought was a great opportunity for the American people to see two very different visions for the country. And I think it was helpful to be able to describe those visions," he said.

POLL BOOST FOR ROMNEY

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, wrote 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.

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," 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 European crowds during his historic 2008 election bid.

"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 new ads hoping to capitalize on Romney's momentum. One had him presenting his plan for creating 12 million new 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. TheDow Jones coal index was 5.05 percent higher.

But shares of U.S. hospital operators fell as Romney's strong showing raised doubts about the future of Obama's 2010 healthcare reform.