Virginia gubernatorial candidates Democrat Terry McAuliffe, left, and Republican Attorney General Ken Cuccinelli debate Sept. 25, 2013, in McLean, Va. (Linda Davidson/The Washington Post)

Two new polls in the Virginia governor’s race show Democrat Terry McAuliffe leading Republican Ken Cuccinelli II in a close contest with just 32 days to go.

A new Hampton University poll found McAuliffe up 5 points over Cuccinelli. The survey of likely voters — an inaugural effort by the Hampton University’s Center for Public Policy — found that McAuliffe has 42 percent support compared with 37 percent for Cuccinelli, largely because of McAuliffe’s sizable backing from women and African-American voters.

Robert Sarvis, a Libertarian, received 8 percent support. The poll showed that Sarvis has attracted interest across the board and draws almost evenly from Democrats and Republicans.

The poll found that the races between the GOP and Democratic candidates for lieutenant governor and attorney general are as close or closer. The poll’s overall margin of error was 2.9 percent.

A separate poll by the University of Mary Washington on Friday found McAuliffe ahead of Cuccinelli by 7 points among likely voters, 42 percent to 35 percent. Sarvis picked up 10 percent in the Mary Washington poll.

Among registered voters, the Mary Washington poll found McAuliffe leading 43 percent to Cuccinelli’s 33 percent. Sarvis polled 9 percent support among the survey’s 823 registered voters. Among registered voters, the error margin was 3.9 percent.

In the downballot races, Mary Washington’s survey showed the Republican candidate for lieutenant governor trailing his Democratic rival. The same poll showed the Republican nominee for attorney general moving ahead of the Democrat in the race. The poll’s overall margin of error was 3.5 percent. Among likely voters, the margin of error was 4.7 percent.

The Hampton University and Mary Washington polls are also only the latest suggesting that Virginians are less than thrilled with their choices in the gubernatorial race.

“I would say it’s definitely up for grabs,” said Ronald Lester, a Democratic pollster with Lester and Associates who worked as a consultant to the Hampton University poll. Lester said Thursday that the key to the race will depend on who can convert independents in Northern Virginia and Hampton Roads with only about a month to go.

“A month is a lifetime in politics,” said Stephen Farnsworth, professor of political science and director of Mary Washington’s Center for Leadership and Media Studies. “And the figures show that the race is still close.”

The Hampton University poll showed McAuliffe with big leads in Washington’s suburbs, such as Arlington, Fairfax and Prince William counties, while Cuccinelli is ahead in the Northern Virginia exurbs of Loudoun, Fauquier and Spotsylvania counties. In Washington’s suburbs, McAuliffe received 50 percent compared with Cuccinelli’s 29 percent; Cuccinelli led McAuliffe 45 percent to 33 percent in the exurbs.

The Mary Washington poll also suggested that McAuliffe was running strongest in Northern Virginia and Tidewater, but found Cuccinelli with his strongest support in the northwest region of the state.

Both polls showed McAuliffe well ahead among women voters.

The Mary Washington survey had McAuliffe up 18 points — 48 percent to Cuccinelli’s 30 percent — among likely women voters. The Hampton University poll found a 15-point gender gap. Among women, McAuliffe received 47 percent support, compared with Cuccinelli’s 32 percent, in the Hampton University poll.

Among white women, McAuliffe and Cuccinelli are in a virtual dead heat, with 41 percent to 40 percent, respectively, the Hampton University poll found. Among African-American women, however, McAuliffe far outruns Cuccinelli, 72 percent to 2 percent, according to the Hampton University poll.

Like others, the Hampton University survey found that Virginians have a mostly negative view of the two major-party candidates. Thirty-one percent had a favorable view of McAuliffe, while 37 percent had an unfavorable view of him. For Cuccinelli, about 33 percent gave him a favorable rating, while 47 percent had an unfavorable view. Each candidate received overall positive ratings in only one of seven regions in the Commonwealth: for McAuliffe, it was the Southeast; for Cuccinelli, the Southwest.

The Mary Washington poll found that 52 percent of likely voters had an unfavorable view of Cuccinelli, while only 36 percent had a favorable view. McAuliffe’s unfavorable rating was 35 percent, compared with a favorable view among 38 percent.

The campaign’s negative tone continued this week as McAuliffe, a former Democratic National Committee chairman and businessman from McLean, and Cuccinelli, who is the state’s attorney general, attempted to link each other to Washington’s political dysfunction.

McAuliffe has badgered Cuccinelli to denounce Sen. Ted Cruz (R-Tex.), a tea party hero who sparked the Capitol Hill fight. Cruz and Cuccinelli will be making a joint appearance this weekend at the Family Foundation’s annual gala in Richmond.

“Ken Cuccinelli has made it clear that he cares more about Ted Cruz and the Tea Party than he does about Virginia’s economic well-being,” McAuliffe campaign spokesman Josh Schwerin said Thursday in a statement. “With the majority of Virginia’s congressional delegation and Bob McDonnell rejecting the continued use of shutdown as a bargaining chip and Republican senators turning on Ted Cruz, Ken Cuccinelli is standing alone in support of the architect of the shutdown.”

Cuccinelli has said more than once that he opposes a shutdown but has refrained from criticizing Cruz. On Thursday, Cuccinelli said that he believed it was time for Congress to move on.

“Strangling government to do this is not an appropriate course to go,” Cuccinelli told reporters. “I certainly would like to see the health-care bill scaled back or repealed. But I also think we need to keep functioning as a government. Some people think we’re a superpower. We need to act like it. I don’t see that happening on the other side of the Potomac.”

Cuccinelli has also been hammering McAuliffe as a creature of inside-the-Beltway politics who had threatened to hold up a state budget unless it includes an expansion of Medicaid as part of the Affordable Care Act. Cuccinelli also has emphasized McAuliffe’s support for Obamacare and the health law’s less-than-smooth launch this week.

“I think it’s fair to say that both McAuliffe and Cuccinelli have done a good job running each other’s negatives up,” said Lester, who teamed with Kellyanne Conway, a Republican pollster with the Polling Company.

Those high negatives have helped make Sarvis something of a wild card in the race. He received 58 percent of his support from independents, 22 percent from Democrats, and 21 percent from Republicans, the Hampton University survey found.

The Hampton University survey used live interviews with 800 likely voters from Sept. 25-26 and Sept. 28-29. The Mary Washington poll surveyed 1,001 Virginians, including 823 registered voters, from Sept. 25-29.

Farnsworth said the Mary Washington poll was being conducted when people were only talking about a possible shutdown of the federal government. Now that it’s happened, it’s likely to make Cuccinell’s uphill path even rockier, Farnsworth said.

“The wave of attack ads and the governor’s troubles created a harsh headwind for Cuccinelli – and now things are even worse with the government shutdown,” Farnsworth said in an e-mail.

On downballot races, the Mary Washington poll found that Sen. Ralph Northam (D-Norfolk) had opened a 4-point lead over GOP nominee E.W. Jackson in the lieutenant governor’s race. Northam’s lead was wider — 40 percent to 32 percent — among registered voters, the Mary Washington poll found.

In the attorney general’s race, the Mary Washington poll showed that Sen. Mark D. Obenshain (R-Harrisonburg) was running ahead of Sen. Mark R. Herring (D-Loudoun) by a margin of 42 percent to 36 percent among likely voters. Obenshain was leading by only 2 points, 38 to 36 percent, among registered voters.

The Hampton University poll found tighter races among candidates for lieutenant governor and attorney general, probably because they are less well known.

In the lieutenant governor’s race, the poll found that Jackson and Northam were in a statistical dead heat: Jackson received 39 percent support, compared to Northam’s 38 percent. Twenty-three percent are undecided. The poll found that heavy majorities still say they do not know enough about the two men to form a favorable or unfavorable opinion of them.

In the attorney general’s race, the survey found that Obenshain had taken a 4-point edge over Herring, with 41 percent compared to 37 percent. Twenty-three percent are undecided.

The Hampton University poll is the first from its Center for Public Policy, which plans to conduct other surveys on subjects such as education, health care, transportation, violence and education.

“We believe this is going to be a great foundation for future polls,” Kelly Harvey Gill, director of the Center for Public Policy, said. “We want to take the pulse of the people of Virginia.”

Staff writer Laura Vozzella contributed to this report.