President Barack Obama has accused Mitt Romney of being dishonest, after a televised debate that most observers agreed his Republican rival won.

Speaking in Denver, Colorado, Barack Obama urged his rival to tell the “truth” about his own policies.

An estimated 40 million people watched Wednesday’s debate, according to the Nielsen TV ratings service.

The Obama campaign has said there will be some “adjustments” in strategy before the election on 6 November.

A Reuters/Ipsos poll on Thursday suggested Mitt Romney had a net positive rating for the first time in the presidential campaign.

The poll said 51% of voters viewed him positively, with Barack Obama at 56%. The Republican moved ahead of the president on which candidate voters trust to handle the economy, create jobs and manage the deficit.

Barack Obama told a rally of some 12,000 supporters on Thursday: “When I got on to the stage, I met this very spirited fellow who claimed to be Mitt Romney.

“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.”

Mitt Romney repeatedly denied the $5tn claim during Wednesday night’s head-to-head.

Fact-checkers have said that Mitt Romney’s proposal to lower taxes by 20%, abolish estate tax and the alternative minimum tax would reduce revenue by $5 trillion over a decade.

The Republican has said he would help offset that by eliminating tax loopholes; the non-partisan Tax Policy Center says the sums do not add up.

Barack Obama told Thursday’s rally: “So Governor Romney may dance around his positions. But if you want to be president, you owe the American people the truth.

“So here is the truth. Governor Romney cannot pay for his $5 trillion tax plan without blowing up the deficit or sticking it to the middle class. That’s the math. We can’t afford to go down that road again.”

The Democratic president also mocked Mitt Romney’s plan to cut government subsidies for the PBS television channel that produces Sesame Street.

Mitt Romney said during the debate: “I love Big Bird”, adding that would not stop him axing federal funding to the public broadcaster.

“Thank goodness somebody is finally getting tough on Big Bird,” Barack Obama told Thursday’s rally.

“It is about time. We didn’t know that Big Bird was driving the federal deficit.”

Mitt Romney campaign spokesman Ryan Williams dismissed the president’s attack.

“In full damage-control mode, President Obama today offered no defence of his record and no vision for the future,” he said.

Barack Obama strategist David Axelrod told reporters on a conference call that the campaign would now rethink its strategy.

“We are going to take a hard look at this,” he said.

“I’m sure we will make adjustments as to where to draw the line in these debates and how to use our time.”

Mitt Romney is also back on the campaign trail, appearing at a conservative fundraiser in Colorado on Thursday morning.

Amid sustained cheers, the Republican hopeful told supporters they would have to “go out and knock on doors, and get people who voted for President Barack Obama to see the light and come join our team”.

The candidates went head to head on Wednesday for 90 minutes on jobs, taxes and healthcare.

Opinion polls agreed that Mitt Romney had the upper hand in the debate – the first of three between the White House rivals.

Various surveys gave Mitt Romney a 46-67% margin, with Barack Obama trailing on 22-25%.

The president was criticized for appearing hesitant and subdued, while the former governor – who has been lagging in the race – seemed animated and assertive.

Vice-presidential candidates Joe Biden and Paul Ryan will meet in Danville, Kentucky on 11 October, before the second presidential debate on 16 October.