When McCaskill got to the lectern, she reminded everyone that she was a local girl, originally from the Ozarks. Then, avoiding even the word “Republican,” she said, “We have got to be very careful going down this road. It’s not going to be enough to complain about them. We’ve got to remind people what we’re for.” But she did complain about Republicans, saying that they have slashed health-care benefits, given tax cuts to the rich, imposed tariffs on American corn and soybeans and pork, allowed pharmaceutical companies to overcharge for prescription drugs, and threatened public education and union organizing. “We stand with the people who take a shower after work, and not before work,” she declared, as the audience cheered. “We stand with the men and women who try to make it work every month.”

McCaskill deftly filleted Josh Hawley, who has been in his job since 2016, by implicitly contrasting her years of experience with his jejune overconfidence. “Let’s talk about Josh,” she said. “Josh made two promises when he ran for attorney general. He looked at the camera and said, ‘I’m not a politician. I’m not running for one office to turn around and run for another.’ ” Yet here he was, two years later, running for the Senate. “The second promise he made was that he was going to go after public corruption. How’s that worked out?” Hawley had been slow to investigate corruption charges against state officials, including Missouri’s former Republican governor Eric Greitens, who resigned last May, after a woman with whom he was having an extramarital affair accused him of sexual assault. (Greitens denies the assault.) McCaskill is very good at convincing people that she’s more candid and less high and mighty than most politicians. Continuing her remarks about Hawley, she said, “He looks good!” Hawley is slim and muscular, attributes that don’t necessarily matter to Missouri voters. “I didn’t go to Yale Law School”—Hawley’s alma mater. “I went to Mizzou Law School, but I can keep up.” She said that she had worked as a waitress to help pay for school, then talked about fund-raising: “My average donation is seventy bucks. Hawley’s average donation, it has a comma in it. That’s the difference.” (She was exaggerating for effect—Hawley’s average donation doesn’t actually have a comma in it.)

Eventually, she got to Trump. “When I’m at the grocery store,” she said, “before I even get to the butcher—I’m still in produce—some people used to walk up to me and say, ‘Hi, Claire, I think you’re doing a good job,’ or maybe they don’t think I’m doing a good job. You know what they do now? They grab me and say, ‘Save us! Please save us!’ ” This was extra-points political practice: McCaskill was planting the idea that Trump is a horror without owning the criticism, while also indicating that she lives pretty much the same kind of life her constituents do. She said that in the state legislature, where she was known for cursing with abandon, her senior colleagues put a swear jar on her desk. We ought to have a Trump swear jar, she said. “When people come up to you and start talking about Donald Trump, you need to tell them about the Trump swear jar. They have to put five dollars in the Trump swear jar every time they want to talk about Donald Trump. The Trump swear jar is located at ClaireMcCaskill.com!” The audience roared.

Southern Missouri was once staunchly Democratic, but in the course of McCaskill’s life it has been moving steadily to the right. When I met with her in Washington, she told me that she first began to realize that her family was out of step with its neighbors when Kennedy ran for President, in 1960. “Dad was a Democratic committeeman, and somebody threw a rock through the window of the county Democratic headquarters. It was bigotry—about [J.F.K.’s] being a Catholic.” She recounted the history of the country’s political realignment: “There was a cataclysmic shifting when we decided that civil rights was the cause of our party. Missouri, along with the traditional Democratic Southern states, began to shift.”

In the nineteen-eighties, when she was in the state legislature, there were still rural Democrats who felt that the Party cared about their economic interests and Republicans didn’t. “No more,” McCaskill said. “Now there’s a much brighter dividing line between rural and urban. A lot of people gave up on me. They gave up on us.” She acknowledged the seductive simplicity of Trump’s message. “There used to be a way to work your way up from the mailroom. Now there’s no more mailroom,” she said. “Donald Trump gave voters a place to put their anger.”

By the time McCaskill was in ninth grade, at Hickman High School, in Columbia, she had set her sights on becoming the first female governor of Missouri. During a speech contest, she gave a talk condemning the Ku Klux Klan, and felt “the incredible high when the thunderous applause came at the end of the speech.” When she was a senior, she ran in her first election, for homecoming queen. In her memoir, she describes the event as a formative experience in retail politics. The voters were the members of the football team, and she launched a months-long campaign to win them over. “I paid them special attention, did favors, arranged dates,” she writes, and “although I wanted others to believe I won because I was popular, in fact I had carried out an effective political operation by identifying a constituency and working hard to gain its support.” She practices grownup politics the same way: be practical, be clever, don’t venture too far left or right, and work harder than anybody else.

Under the old rules, McCaskill would have built-in advantages this year: the President’s party usually loses seats in Congress in a midterm election, and voters tend to stick with incumbents. In national generic surveys, the Democratic Party has been consistently beating the Republican Party, by more than ten points in some polls. The question is whether politics has changed. The polarization of the electorate has been increasing for a generation; people used to be far more comfortable voting for a President from one party and a senator from the other. Gary Jacobson, a political scientist at the University of California, San Diego, and a leading expert on congressional elections, says that the advantage for an incumbent has fallen from eight or nine points to two or three—the lowest it has been in decades. And that situation leads to another question: If there aren’t as many swing voters as there used to be, should each party respond by pursuing a more ideological approach, looking past local issues and trying to awaken the unruly passions of its voters? This is a question that political spectators have spent the year debating; for McCaskill, it’s a matter of political life and death.

Like many successful people, McCaskill has the ability to stay focussed on one thing. In 1971, she entered the University of Missouri, where she majored in political science, and decided to stay there for law school, because, she writes, “I knew that being part of the network of lawyers in Missouri would help me more with any future political campaigns.” After graduating from law school, in 1978, she worked in an appeals court in Kansas City, and then, in 1982, she ran for the state House of Representatives, and won. She was one of twenty-five female legislators, and one of two female lawyers. “She came in as a firebrand,” Gracia Yancey Backer, who joined the legislature at the same time, told me. “She had to fight the good old boys.” One high-ranking colleague called her a whore on the floor of the House, and another told her that if she wanted his help with a bill she’d have to bring her kneepads. McCaskill made crime her signature issue, successfully proposing a “bill of rights” for crime victims and a tightening of parole eligibility for people convicted of violent crimes. Her positions gave her a tough image in the male-dominated legislature and, as she proudly reports in her memoir, earned her the nickname Hang ’em High Claire.