WASHINGTON » Mitt Romney is seen by more voters in three battleground states as a strong leader after his dominant debate performance last week, but perceptions that the economy is improving remain a firewall there for President Barack Obama as the 2012 campaign comes down to its final weeks.

The latest Quinnipiac University//CBS News poll, of likely voters in the three states, Colorado, Virginia and Wisconsin, found no sharp movement after the debate and the news last Friday that the unemployment rate in September had dropped below 8 percent for the first time since Obama took office.

But the poll suggested that Romney had gained strength in a number of ways since last month and that Obama’s best defense is the somewhat brighter economic outlook and the fact that voters continue to relate to him more than they do to his opponent.

Romney’s backers now support him more fervently than before. He is running stronger in particular among those who say they are paying especially close attention to the race. He retains his dominance on the issue of handling the federal budget deficit and seems to have stabilized his showing on handling of the economy.

About two-thirds of the voters in each state said Romney has strong leadership qualities, more than said the same of the president.

"The debate made me feel better about" Romney, one poll respondent, Paula Gregory, 37, a clerical manager for a construction firm who lives in Highlands Ranch, Colo., said in a follow-up interview. "I had more specific information from him and he had real rebuttals to accusations that had been made, most specifically about his tax plan."

But Obama holds a slim advantage in Virginia and Wisconsin, and remains tied with Romney in Colorado, perhaps, in part, because voters are growing increasingly hopeful that the country’s economy is turning around. That conclusion follows last Friday’s report showing the unemployment rate falling to 7.8 percent, the first dip below 8 percent since January 2009. In Virginia, 42 percent of voters say the economy is getting better, up from 24 percent in July; in Colorado the figure is 37 percent, up 11 points in three months.

The positive economic news appears to have buffered the president in Virginia, Wisconsin and Colorado from the substantial improvement in Romney’s national poll numbers over the past week. The three battleground polls suggest that challenges remain for Romney in the next 26 days even as his supporters express new confidence about their candidate.

"It’s slow and steady, but the job market is growing," Thomas Broderick, 50, a doctor from Madison, Wis., said in a follow-up interview. "Also, from what I see around my city, the housing market is better. People are able to sell their homes. Houses are being built. If the economy were in the tank, perhaps it would be harder to vote for Obama."

In Virginia and Wisconsin, Obama maintains double-digit leads over his rival when voters are asked which candidate cares about their needs and who would do a better job for the middle class. The preference for Obama on those issues is smaller in Colorado, a state where the two candidates have been virtually tied for months.

The president’s support is built on strengths that have been evident for months. In the two states where he holds an advantage overall, Obama has consistently outperformed Romney on a series of issues, including international affairs, health care and Medicare.

And in those states, Obama’s months of advertising attacking Romney’s character appears to have worked. The president maintains significant leads over Romney on the issue of trust and honesty. Nearly 60 percent of voters in Virginia and Wisconsin say Obama is trustworthy and honest; just 47 percent say the same of Romney.

Suzanne DiLisi, 44, a restaurant worker from Marshall, Va., said Wednesday that she planned to vote for Obama because of concerns that Romney would not help lower-income people like herself.

"Financially speaking, I believe Romney will cut the debt," DiLisi said. "But he will do it at the expense of people who are already suffering."

She pointed to Romney’s comment that 47 percent of Americans are dependent on government.

"Those remarks, they were awful," she said. "As president, you literally have to work for the very poor to the very rich."

The , in collaboration with Quinnipiac University and CBS News, is tracking the presidential race with recurring polls in six states. The current surveys, which have margins of sampling error of plus or minus 3 percentage points for each candidate, were conducted from Oct. 4 to Oct. 9, after the debate in Denver.

Officials with both campaigns expressed confidence about success in Virginia and Wisconsin. Romney’s campaign hopes that his selection of Rep. Paul D. Ryan of Wisconsin as his running mate will help him in a state that Obama won decisively in 2008. In Virginia, Obama and Romney have each fielded intensive on-the-ground operations and millions of dollars in ads.

Romney’s campaign is targeting the state’s traditionally Democratic coal country, its military-heavy communities of Virginia Beach and Newport News, and Asian population centers in Northern Virginia, officials at the campaign said.

"There’s no area of Virginia that’s off the table," said Gov. Bob McDonnell, a Republican, who won three years ago by earning support in those same parts of the state. "Overwhelmingly in Virginia, it’s jobs and spending. I think that Mitt Romney’s message works everywhere."

Obama’s campaign strategists said the president was working hard to repeat his 2008 victory in the state. He has visited Virginia 44 times since becoming president, officials said.

"It was always going to be close," said Rep. Gerald E. Connolly, D-Va.

He said fundraising and enthusiasm had actually picked up since Obama’s disappointing debate performance.

"It helped Romney. But there’s a counter-reaction, too. And it’s not deflation. It’s a call to arms."

The picture is a bit different in Colorado, where support for the two candidates is evenly divided across a broad series of issues. Romney fares better in Colorado among women than he does in the other two states.

"We are basically sitting at a statistical tie today," said James Garcia, Romney’s state director in Colorado. But he said enthusiasm for Romney had surged since the debate, in Denver. "Volunteer enthusiasm is through the roof."

The new polling in Colorado backs that up. Six out of 10 Romney voters in the state now say they are strongly favoring him rather than offering lukewarm support or just opposing Obama. Earlier this summer, just over half of his voters said that.

HOW THE POLLS WERE CONDUCTED

The latest Quinnipiac University//CBS News polls included telephone interviews conducted Oct. 4 through Oct. 9 with a total of 4,449 adults in Colorado, Virginia and Wisconsin. Of these, 4,089 said they were registered to vote.

Results are based on 1,254 likely voters in Colorado, 1,288 likely voters in Virginia and 1,327 likely voters in Wisconsin. Likely voters are adults who say they are registered to vote and will "definitely" vote on Election Day.

All interviewing was conducted from the Quinnipiac University Polling Institute in Hamden, Conn. Interviews were in English or Spanish.

The telephone numbers called, both landlines and cellphones, were from random digit dialing samples provided by Survey Sampling International of Shelton, Conn. The regions within each state were represented in proportion to their share of all telephone numbers. Random digits assured access to listed and unlisted numbers alike. The completed samples were adjusted to assure the proper ratio of landline-only, cellphone-only and dual-phone users. Within each household, one adult was designated by a random procedure to be the respondent for the survey.

Interviewers made multiple attempts to reach every phone number in the survey, calling back unanswered numbers on different days at different times.

Each state’s results have been weighted to adjust for variation in the sample relating to region, sex, race, Hispanic origin, age and education.

In theory, in 19 cases out of 20, overall results based on such samples will differ by no more than 3 percentage points in either direction from what would have been obtained by seeking to interview all voters in each of the states. For smaller subgroups, the margin of sampling error is larger. Shifts in results between polls over time also have a larger sampling error.

In addition to sampling error, the practical difficulties of conducting any survey of public opinion may introduce other sources of error into the poll. Variation in the wording, order and translation of questions, for example, may lead to somewhat different results.

Michael R. Kagay of Princeton, N.J., assisted The Times in its polling analysis. Complete questions and results are available at nytimes.com/polls.

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