With the first debate of the U.S. presidential campaign behind them, President Barack Obama and his Republican challenger, Mitt Romney, headed back to their cross-country travels Thursday, seeking voters' support for next month's election.

Mr. Romney is holding a rally in Virginia with his running mate, Congressman Paul Ryan. Mr. Obama began his day in Denver, Colorado, the site of Wednesday night's debate, and he will travel later to Wisconsin, Mr. Ryan's home state.

During the debate former Massachusetts governor Romney said Mr. Obama's policies have weakened the American economy and increased the national debt. He contended the president, if re-elected, would increase taxes and raise government spending to worsen the federal deficit.

Many observers said Mr. Romney “won” the debate, and they predicted his campaign would be re-energized by the Republican's aggressive stance against the incumbent Democratic president.

Mr. Romney said middle-income Americans have been “buried” or “crushed” under high taxes. He contends tax rates on both corporations and individuals must be reduced.

Mr. Obama countered that Mr. Romney's tax plan would favor wealthy Americans and force severe cutbacks in important domestic programs.

The president says the first role of the federal government is to “keep the people safe,” but it also should create “frameworks” in which people can succeed. He noted that, in the past, the government has helped create railroads, research institutions and educational institutions.

The two men also sparred about the health-care reform law Mr. Obama pushed through Congress. Mr. Romney once again pledged that he would repeal the law, commonly known as “Obamacare,” if he were elected. He criticized the president for focusing on health care rather than the economy during Mr. Obama's first years in office.

Mr. Obama said the need to reform the U.S. health-care system was and is a key issue for all Americans – business owners and individuals.

In his closing statement, the president said he wants to expand the accomplishments of his first four years in the White House. He said he will work for change just as hard in a second term as he did in his first.

Mr. Romney, who had the last word in the nationally televised debate, said re-electing the president would mean more hardship for the American middle class.

Political analysts are awaiting the result of post-debate surveys of voters' feelings about the presidential race. In recent days Mr. Obama appeared to be leading Mr. Romney, in part due to adverse public reaction to the airing of private remarks in which the Republican candidate said he would not expect support from nearly half of the American electorate that is financially dependent on government benefits.

The two candidates will meet for another debate on October 16 – a town hall-style session in which they will take questions from audience members.