Hillary Clinton clinched the Democratic presidential nomination June 6, making her the first woman in history to lead a major party. (Victoria Walker/The Washington Post)

Hillary Clinton has been part of our national consciousness for so long that it is easy to forget how far she has pushed the edges.

It is not just that she has made history by becoming the first woman to claim the presidential nomination of a major party. Hillary — known on a first-name basis, both by her fervent supporters and by those who despise her — has been the avatar of a different way of thinking about women and what they can do.

Hers was an earnest generation of feminists who decided that nothing was beyond them. They could choose their careers, build unshakable marriages and raise nearly perfect children. They could go out and change the world, yet still be there for their friends.

A younger Hillary once said: “There is no formula that I’m aware of for being a successful or fulfilled woman today. Perhaps it would be easier . . . if we could be handed a pattern and cut it out, just as our mothers and grandmothers and foremothers were. But that is not the way it is today, and I’m glad it is not.”

Not all of those plans worked out for the women of her generation, of course. And even when they did, the price to be paid was high.

So it is that Hillary, for the past 20 years in a row, has been voted the most admired woman in the world in an annual Gallup poll. And yet she enters the general-election campaign with the highest negatives ever seen in a Democratic presidential ­nominee.

The arc of her career has not been a graceful one. Again and again, the sequence has been the same: She sets out, stumbles, gets up again, grinds on.

And as she herself has acknowledged, she lacks the natural political talents of the two men against whom she is inevitably measured — the one she married, and the one to whom she lost in 2008.

When she ran against Barack Obama, he was seen as the historic figure. So caught up was everyone in hope and change that it was little noted at the time that Hillary was the first woman of either party to win a state in a primary. (Obama was not the first African American to do so.)

It was not until she conceded defeat that she found her voice — and turned everyone’s attention to the fact that something significant had happened.

“Although we weren’t able to shatter that highest, hardest glass ceiling this time, thanks to you, it’s got about 18 million cracks in it,” she said. “And the light is shining through like never before, filling us all with the hope and the sure knowledge that the path will be a little easier next time.”

Cutting that path, she has sometimes gone over the edge.

As first lady, she took over her husband’s most ambitious domestic policy initiative — transforming the health-care system — and nearly brought down his presidency when she failed.

In the years that followed, she rarely set foot in the West Wing. Instead, she put her efforts at home into initiatives that would not set off alarms. She wrote a surprise bestseller about raising children, “It Takes a Village.” And when she did speak out, it was overseas — most memorably, calling for human rights for women in ­Beijing.

Her friend Diane Blair once told me: “She was trying to figure out how she could be who she is — a thinker, a doer — without arousing hostility from those who felt she was overstepping her bounds.”

And there was always the asterisk on her achievements: She wouldn’t be where she is if she hadn’t married who she did.

But then, it could also be argued that Bill Clinton would not have made it to where he did if Hillary Rodham had chosen someone else.

When the 1980 election suddenly transformed him from the youngest governor in the United States to the youngest ex-governor, it was pragmatic, disciplined Hillary who took charge and decided what had to be done to bring him back.

She brought in new advisers and demanded a new game plan. She also took his last name, got rid of her glasses and ­went blond.

Nearly two decades later, Clinton’s self-destructive tendencies nearly brought him down again. And once again, it was Hillary who saved him.

She stood by him, endured the humiliation, and in doing so, found herself more well-regarded than she had ever been.

That, ironically enough, produced the opportunity that brought her to where she is, setting her on her way to a political career of her own.

On the very day in February 1999 that the Senate was voting to acquit Clinton in his impeachment trial, Hillary was huddling at the White House with adviser Harold Ickes, plotting out an audacious strategy to run for the Senate in New York, a state where she had never lived.

She leveraged her celebrity, won that seat easily, and won it again. And in doing so, she went from being a trailblazer to part of the old order. Thought to be the presumptive favorite in 2008, she once again defied expectations — this time, in a bad way.

Her campaign operation was bloated and inept. The electorate was looking for someone new and fresh.

When it was over, she did what she had done so many other times. She picked herself up and went for the opportunity that presented itself, working for the president who had defeated her.

It was never much in doubt that she would try again, because that is her laborious way. She is determined to make history, and she has; what she will never do is make it look easy.