Jill Biden got attention from supporters, as well as Harrisburg, Pa.’s entire press corps, on Monday at the local Obama campaign office (SEAN SIMMERS/FOR THE WASHINGTON POST)

There’s the scripted world of national politics and then there’s Jill Biden.

The vice president’s wife will take her spot in the front row at her husband’s debate Thursday night in Kentucky but only after a full day of teaching at Northern Virginia Community College. This week is midterms.

Politics is Joe’s thing, Biden has said. Teaching is hers.

Yet, in recent weeks, she has been doing more and more of his thing, becoming an integral part of her husband and President Obama’s reelection campaign.

Unlike Joe, Jill rarely makes the kind of verbal missteps that have become a part of the vice president’s political narrative. Republicans seem always at the ready to pounce on the next possible gaffe of the loquacious ad-libber.

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Jill, who has been married to Joe for 35 years, has a different approach. Behind a lectern, she can seem stiff and studious, like the instructor she is. Even after 13 campaigns for her husband and son Beau, who serves as Delaware’s attorney general, she is still not quite comfortable speaking to crowds. Some say that this slight awkwardness and the absence of campaign-slick tactics are assets.

“She could be your mother, your friend, your sister, your neighbor. It’s that feeling you get with her,” said Stephanie Cutter, deputy manager of the Obama campaign. “The sign of a good campaigner is to make people think that you’re not campaigning.”

The Obama campaign, which refers to the second lady as Dr. Biden in a nod to her 2007 doctorate in education from the University of Delaware, has set up Biden, 61, as its everywoman. Since her steady performance introducing her husband at the Democratic National Convention last month, the campaign has sent Jill Biden to about 20 second-tier and suburban markets in Pennsylvania, Michigan, New Hampshire and Minnesota, where it is trying to reach women and rally supporters.

At the same time, Biden has carved out a rare place in the annals of political spouses. Each Tuesday and Thursday, she spends a full day at Northern Virginia Community College, where she teaches entry-level English. The grandmother of five also makes time to babysit, as she did in Wilmington, Del., last weekend. She and Joe have three grown children, daughter Ashley and sons Beau and Hunter, whom Jill adopted when she married Joe, a young widower who had recently been elected to the U.S. Senate.

“She just makes it work,” Beau Biden said of his mom’s full schedule. “She’s just tough, and when she dives into something — like she has — she is going to find the time to make it work.”

At the community college, her students know her as “Dr. B.” When they ask whether she is related to Joe Biden, she says, “Yes,” acknowledging only that he is a relative. She works out of a cubicle in an office with 60 other faculty members and helped start a mentoring program for women at risk of dropping out of the college. At her request, her Secret Service detail dresses as students — although their earpieces sometimes draw attention.

“She demanded no special treatment,” said Jim McClellan, dean of the college’s liberal arts division and Biden’s boss. “She wants to be treated like a member of the faculty.”

At campaign stops, Biden introduces herself as “a lifelong educator and military mom,” referring to Beau’s service in Iraq. Despite detractors, she has taken the title “Dr. Biden,” saying she earned it and never much liked being called “Mrs.” But one-on-one, she introduces herself as “Jill.”

She is one of a handful of ­vice-presidential wives to keep their day jobs, including Lynne Cheney, who continued her work as a scholar at the American Enterprise Institute, and Marilyn Quayle, who served on the board of the Federal Emergency Management Agency.

“It’s a weird role, second lady, even the very unofficial title is slightly demeaning,” said ­first-lady historian Carl Sferrazza Anthony. “What is unique and what gives [Biden] a naturally wider visibility is that the project on behalf of military families is done jointly with Mrs. Obama.”

The White House’s initiative to support military families, along with a children’s book that Biden wrote about Beau’s year serving with the National Guard in Iraq, have also brought her a star turn playing herself on the television show “Army Wives,” interviews on daytime talk shows and joint magazine covers with Michelle Obama.

Separately, Biden launched a bus tour of community colleges for the Obama administration this year that took her to corners of the country that rarely see a national political figure, including Wytheville Community College in southwestern Virginia and Davidson County Community College outside of Greensboro, N.C. Apart from spending time with her family, it is among community colleges teachers and students and with military families that Biden feels most comfortable, aides said.

“So many people have this feeling that people run for office because they want to ride in a limousine,” said former U.S. senator Ted Kaufman (D-Del.), Joe Biden’s former chief of staff, a longtime friend of the family and Biden’s successor in the Senate after he was elected vice president. “That’s not true of a lot of people, and it’s especially not true of Jill Biden.”

That’s one reason the Obama campaign views her as a bonus. Her visits sometimes draw as few as 40 people, but they often make the front pages of local newspapers. In Harrisburg, Pa., this week, her visit brought the city’s entire press corps to the Obama campaign’s office. There, she read from notes and spoke to 183 people for 10 minutes about such issues as health-care reform and equal pay for women.

“For women of my generation, we do not want to go back and refight those battles that we fought decades ago,” she said as the crowd clapped.

“We’ve seen the unemployment rate go down,” she added, gesturing downward. “You probably saw that on Friday.”

After the rally, where she was accompanied by daughter Ashley, Biden lingered for nearly 20 minutes, talking and taking pictures with those who came to see her. There were no metal detectors, and the crowd was separated from her by a line of blue tape on the ground, not ropes.

“She was down to earth, very personable,” said Dianne Harper, a community college instructor who snapped photos of Biden on her disposable camera.

Another woman held up a copy of Military Spouse magazine, featuring Michelle Obama and Jill Biden on the cover. The second lady signed it.

Shortly before her official motorcade of four vehicles — small compared with the vice president’s train of SUVs and vans — pulled out, a bearded man introduced himself as a veteran. He thanked Biden for her work on behalf of military families and said: “Now I’ve shaken your hand and your husband’s hand. Make sure you tell him in the debate to call Paul Ryan, ‘Republican Ryan’ not ‘Congressman Ryan.’ ”

Biden smiled but said nothing.