DENVER — President Obama has opened a sizable lead over Mitt Romney in polling ahead of the election as both Democrats and Republicans are increasingly convinced that he is going to win re-election, according to The Washington Times/Zogby Poll released Sunday.

In the latest poll, Mr. Obama drew 49.7 percent support while the Republican nominee garnered 41.1 percent. The previous Times/Zogby polls showed the race a dead heat — including just before the national party conventions, when they were tied with 45.7 percent of the vote each. Even with third-party candidates added to the mix, the results barely changed.

• Click here to view poll data (PDF file)

Mr. Obama’s support is growing even as voters are split on whether they are better off than they were four years ago — the key question Mr. Romney poses on the campaign trail — and even as voters said they weren’t happy with the president’s handling of the attacks on U.S. diplomatic posts three weeks ago.

“If Obama were running against himself, ‘Would you vote for Obama, yes or no,?’ this would be a much closer race. To a great degree, it’s all about Mitt Romney right now, and the judgment today is he doesn’t appear to be a suitable alternative, including for people who don’t want to vote for Obama,” said John Zogby, the pollster who conducted the survey.

“Now, it’s not over — oh, absolutely, it’s not over. No prediction here. But [Mr. Romney] is on the ropes,” he said.

The poll of 800 likely voters, taken Thursday through Saturday, has a margin of error of 3.5 percentage points. Those who didn’t have a definitive choice for president were asked which way they leaned, and those were included in the head-to-head tally.

The survey, which was weighted for demographic purposes, tracks with other national surveys that show Mr. Obama gaining momentum as the election nears, and shows Mr. Romney’s window closing.

Indeed, 57 percent of voters now say they expect Mr. Obama to cruise to re-election, which is up 10 percentage points from just before the parties’ national conventions. The higher expectations hold true across the ideological spectrum, with Democrats, Republicans and independents becoming more convinced of Mr. Obama’s success.

Analysts said Mr. Obama got an initial bump out of his convention in early September, and then Mr. Romney stumbled for several weeks, particularly with the release of a video of him telling a closed-door group of donors this year that 47 percent of voters are dependent on government and see themselves as “victims.” He said he didn’t expect to win the support of those people.

Asked in the poll, 41 percent of voters agreed with Mr. Romney — about equal to the support he is getting overall.

Meanwhile, 40 percent of voters, including 68 percent of Democrats and 41 percent of independents, “strongly disagreed” with Mr. Romney’s remark.

Speaking on “Fox News Sunday,” Republican vice presidential nominee Paul Ryan said Mr. Romney had been “inarticulate” with the comment, but added that Republicans believe the president has fostered an atmosphere of dependence on the federal government.

“Here and there, we have not been able to frame that choice as clearly [as we have wanted],” he said. “I really believe that by the end of this day, people are going to understand what they’ve got and the choices that they have.”

The Times/Zogby poll had good news for Mr. Obama across the board. He led Mr. Romney in each of five areas: jobs and the economy, national security, immigration, energy and foreign affairs.

In fact, Mr. Obama has gained ground on every one of those areas since The Times/Zogby poll last asked about them in May, including an 8-percentage-point leap when voters are asked who would do better on jobs and the economy. In May, Mr. Romney led that category 52 percent to 46 percent, but Mr. Obama now leads 49 percent to 44 percent.

Mr. Romney also is hurting because of the number of voters who feel they don’t know him as well as Mr. Obama.

The poll asked voters to rank how well they felt they knew Mr. Romney and Mr. Obama on a scale of one to five, with five being “very well.” About 42 percent ranked Mr. Romney a four or five, while 71 percent ranked Mr. Obama a four or five.

Mr. Zogby said that is both a problem and a potential opportunity, particularly when the two men face off Wednesday in the first debate of the season.

“Essentially, Romney still has a net negative in terms of favorable-unfavorable; however, there’s still a considerable number of people who know him or don’t know him,” he said. “This race should be closer than it is, and perhaps it will be. But right now, Wednesday night couldn’t possibly be more important for a candidate than this Wednesday is for Romney.”

Voters were split on whether they are better off now than four years ago, with 46 percent saying they are and 49 percent saying they aren’t. The rest were unsure.

Female voters were most likely to say they were better off, while married women were least likely to say their lot has improved. Those making more than $100,000 and those making less than $35,000 a year were most likely to say they were better off.

Voters also seemed slightly less likely to want to vote for Mr. Obama after his handling of the attacks on U.S. diplomatic posts last month.

Four Americans, including the U.S. ambassador to Libya, were killed in the attack in Benghazi, Libya, and administration officials have struggled to explain the attack, have provided differing accounts of its cause and their knowledge, and took more than two weeks to say publicly that the attack was linked to al Qaeda.

Asked about the Libya attack and other assaults on U.S. embassies throughout the Muslim world, 39 percent of voters said they were less likely to vote for Mr. Obama, versus 24 percent who said his handling of the situation made them more likely to back him.

Most of those responses came from Republicans already inclined to oppose Mr. Obama, or Democrats who back him. Among independents, there was a slight reticence based on his handling.

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