The survey, conducted by veteran local pollster Margaret Kenski of Arizona Opinion, shows that 52 percent of voters surveyed supported Giffords, while just 34 percent supported Graf. Roughly 10 percent of voters said they were undecided.
"I think the poll shows broad, bipartisan support across the district for Gabrielle Giffords," said Giffords campaign manager Rodd McLeod. "Ultimately, people are looking for someone who can reach across the party aisle and get things done. We've got a Congress that's just not effective."
Graf campaign manager R.T. Gregg said his candidate was still suffering from a hangover caused by negative attacks during the GOP primary, but there's still plenty of time for Graf to bounce back.
"The only poll that matters is the one that voters cast," Gregg said. "We're not going to fall victim to being paralyzed by polls. We've got to get our message out."
While the size of Giffords' lead has varied in the polls that have been released to the public, Graf's support has remained mired in the mid-30s or below in each of them.
Kenski, who has polled the district for more than two decades, says that if Graf is going to turn the numbers around, he has to broaden his appeal to voters.
"He's got to talk about something other than the border," Kenski says. "You can't run on a single issue, and if that's his strategy, he's got a problem."
The Weekly survey found that Giffords was enjoying significant crossover support from Republicans. Only 62 percent of GOP voters said they would vote for Graf, while more than 85 percent of Democrats said they would support Giffords. She was also winning the fight for independents and those registered with other parties, with 55 percent supporting Giffords and just 20 percent supporting Graf.
Giffords was ahead of Graf by 22 points in Pima and Pinal counties, where she had the support of 54 percent of voters. Less than a third supported Graf.
In Cochise and Santa Cruz counties, Graf had a narrow lead, 43 to 42 percent.
The poll also showed a dramatic gender gap between the candidates. Giffords was favored by 59 percent of women, while 26 percent said they supported Graf. Among men, 45 percent favored Giffords, and 42 percent supported Graf.
"This would be a tight race if it weren't for the female vote," Kenski says.
The poll showed that border security was the top issue for 29 percent of CD 8 voters. Asked who they trusted more to handle border security, voters were evenly split, with 39 percent favoring Giffords and 39 percent favoring Graf.
But voters trusted Giffords to better handle every other issue polled by the Weekly. For example, on the subject of the Iraq War, which was the top concern for 20 percent of the voters, 45 percent of the voters had more trust in Giffords, while 29 percent had more trust in Graf.
When it came to improving access to health care, which was the top concern of 17 percent of those polled, 60 percent had more trust in Giffords, while about 20 percent had more trust in Graf.
Third-party candidates had yet to make headway in the race. Libertarian candidate David Nolan had the support of 1.2 percent of surveyed voters, while independent candidate Jay Quick had 2 percent.
The Tucson Weekly/Wick Communications Poll, which surveyed 335 voters in Pima and Pinal counties and 67 voters in Cochise and Santa Cruz counties between Sept. 20 and Sept. 23, has an overall margin of error of 4.3 percent.