Gov. Scott Walker mingles with veterans after giving a speech in Milwaukee on Sept. 24. (M.L. Johnson/AP)

— The group of female University of Wisconsin students pulled out their smartphones the minute they saw Gov. Scott Walker coming, corralling the Republican into a round of selfies. Wearing a stiff smile and a Green Bay Packers jersey bearing his name, Walker reluctantly obliged.

But then it was back to the grimmer work of campaigning. In his third election in four years, Walker is far more worried than he was in previous contests — less confident that he can fend off a challenge from Democrat Mary Burke, who is running a competitive race by targeting slow job growth during Walker’s tenure. Both his gubernatorial record and his potential 2016 presidential aspirations are on the line.

“Rallies and tailgates are wonderful, but in the end we need people on the doors,” Walker said Sunday as he spoke to dozens of Republicans gathered around him in a circle during a Packers game-watching party here. “I need you to reach out to people you have never talked to about politics before — that’s how close this election is.”

Among the class of 2016 GOP hopefuls, Walker is the lone early contender who faces such a critical test Nov. 4. New Jersey Gov. Chris Christie and former Florida governor Jeb Bush are not on the ballot, nor is Sen. Marco Rubio (Fla.) or Louisiana Gov. Bobby Jindal. Rep. Paul Ryan (Wis.) — a key Walker ally — will be easily reelected to the House.

Survival would leave Walker poised to ascend to the top tier of the presidential sweepstakes early next year, touting victories in two general elections and in an unsuccessful recall attempt in 2012 over his reductions in bargaining rights for most public workers.

But first Walker, 46, has to get past Burke, 55, who has remained strong in polling despite a brief uproar over a partially plagiarized jobs proposal put together by a consultant.

A Marquette Law School survey released last week showed 47 percent of likely voters supporting each candidate, erasing a five-point Walker lead in the previous Marquette poll. Independents in particular appear to be breaking toward Burke. A New York Times-CBS News poll from last month showed a similarly tight margin.

Burke has risen because of Wisconsin’s fluid, purple-state politics and on the strength of her noncontroversial biography — a former Trek Bicycle executive and former state commerce secretary. Her Web site and ads highlight her “problem solving” skills, largely avoiding the progressive political tradition of a state that has produced Robert “Fighting Bob” La Follette, Russell Feingold and Sen. Tammy Baldwin (D).

The approach is markedly different from the labor-heavy campaigns of Milwaukee Mayor Tom Barrett, Walker’s failed Democratic opponent in 2010 and 2012. Burke’s chief surrogates are not national union leaders but the Obamas, including first lady Michelle Obama, who has been to Wisconsin twice to campaign with her.

President Obama, eager to pick off star GOP governors in an otherwise difficult year, plans to boost Burke with a visit to Milwaukee in the final days of the race. Former president Bill Clinton will appear Friday with Burke. Both men won Wisconsin twice in their presidential campaigns.

On the GOP side, Walker said Christie has offered to come aboard his campaign bus before voters head to the polls, as have Ryan and Iowa Gov. Terry Branstad (R).

“Don’t take this wrong, but because I’m not a challenger, I don’t really need surrogates,” Walker said in an interview Sunday at a Madison field office. “My problem isn’t name ID or drawing crowds. I need to simply get out there and talk to voters. By and large, this is about me.”

Still, Walker said he might require an infusion of cash from the Republican Governors Association — chaired by potential 2016 rival Christie — to stay in contention. So far, the RGA has spent $6 million in the state.

“Hopefully that comes through,” Walker said. “We are always looking for more help. Our main help has to be the RGA.”

Walker has expressed frustration with Burke’s profile as a pragmatic centrist. His advertising portrays her as a firebrand from Madison, a liberal college town where she serves on the school board.

“Only in Madison is someone who’s not the furthest left on the school board considered a moderate,” Walker said. “The bigger challenge to us is that the in-state media buys into that. When she says she’s socially liberal and fiscally conservative, they print it.”

Burke, in an interview Sunday at her headquarters in Madison, said she expected from the outset that a state that backed Obama could be nudged against Walker by spotlighting the economy.

“People don’t feel like their lives have recovered from the recession,” she said. “They’re concerned that they are not making enough to get by.”

When asked to define her politics, she declined to “put a label on it.”

Burke has deliberately avoided relitigating the governor’s efforts against public-sector unions. “It’s not what people are concerned about,” she said.

Social issues are one area where Burke’s campaign wishes it were doing better. Her team has tried to tag Walker, a Baptist minister’s son who opposes abortion and holds other socially conservative views, as an extremist. But he has avoided being dragged into drawn-out debates on moral questions by NARAL Pro-Choice America and Planned Parenthood, both of which are against him.

When asked what Walker is doing to reach out to female voters, Lt. Gov. Rebecca Kleefisch joked: “You see I’m a woman, right? And I’m on the ticket.” She also said that Republicans are a better fit for the “people who are making household decisions.”

The campaign has included relatively little discussion of an investigation by state prosecutors into whether Walker illegally coordinated with right-wing groups by encouraging donations to a private organization. The case is stalled in the courts, posing more of a threat to an eventual presidential run than Walker’s reelection.

Instead, most of the sparring in the race has focused on the governor’s 2010 pledge to create 250,000 new jobs in his first term — a target he missed by nearly 150,000 jobs.

In the first debate of the campaign, the tussle over the jobs number was the only real drama of the evening. “We don’t have a jobs problem in this state. We have a work problem,” Walker said — a comment that Burke seized upon as evidence of the governor’s disconnect.

Walker’s campaign blames the jobs deficit in part on former governor Jim Doyle (D) and has sought to emphasize Burke’s time as a member of Doyle’s Cabinet. At events over the weekend, he played up new figures from the state showing that Wisconsin added 8,400 private-sector jobs in September.

Burke argues that Walker has failed to keep his word on jobs, and she cites declining income levels for many to illustrate how people are hurting.

Pat Manriquez, 52, could be a case in point. Laid off as a flight attendant for Midwest Airlines after 22 years, she now works for much less as a barista at Bella Caffe Coffee House in Milwaukee.

As she made cappuccinos Saturday, Manriquez said the past few years have been exhausting, personally and politically.

“I’m tired of Scott Walker,” she said. “My sister got laid off the same month as I did in 2009, and she’s working at Wal-Mart. It’s been tough, and I just don’t buy that it’s all going great.”

For Burke, that’s a start.