It was a serious mistake, the result of a class-warfare strategy followed to a fault by a zealous Democrat. But inadvertently, one Hilary’s blunder could open the door to the other Hillary’s rise.

We speak of the attack on Ann Romney by Hilary (one L) Rosen. The fallout raises the odds that Hillary (two L’s) Clinton will end up as Barack Obama’s running mate.

Rosen went way over the line carrying out the White House message that Mitt Romney is waging a “war on women.” Rosen’s accusation that Ann Romney “never worked a day in her life” is the biggest unforced error by Team Obama so far.

The issue caught fire and with Ann Romney taking the high road by saying she respects those who make different choices than she did and by joking about the mayhem of raising five boys, the incident capped her hubby’s best week.

Rick Santorum suspended his campaign, meaning the general election has started with an Obama goof. Two polls showed Romney with a slight lead even before Rosen chimed in.

For the White House, the irony is as thick as the fog of damage control it spewed. In undercutting one of Obama’s biggest advantages — his lead among female voters — Rosen makes it more likely that Clinton, the political Wonder Woman and still a frenemy of Obama, will be tapped to save the day.

I know — Obama doesn’t want to go there. White House aides insist Vice President Joe Biden is staying on the ticket. I believe them, or at least I believe that’s their plan.

I also believe the president would dump Biden in a heartbeat if he concludes that’s the only way to win.

Drafting Clinton, who has said she will resign her post as secretary of state at the end of the term, would be eating crow, but it beats losing.

With her appeal to women and working-class whites, she could practically guarantee Obama victory.

If the economy turns south, and if Mitt Romney makes inroads among women, Obama will have to give the switcheroo real consideration.

The numbers explain why.

According to data compiled by Rutgers University, the number of women voters has been higher than men in every presidential election since 1964. While a majority of men tend to vote Republican, women usually lean Democratic and with bigger numbers. They went for Obama by a huge margin in 2008.

Over 70 million women voted, against 60.7 million men, and women gave 56 percent of their votes to Obama and just 43 percent to John McCain. Men split almost evenly.

By comparison, Democrat John Kerry got 51 percent of a lower turnout among women in 2004 and lost to George W. Bush.

The 2012 race was shaping up like 2008, with one survey finding Obama enjoying an 18-point margin among women.

Then Rosen dropped her bombshell on CNN. She has close ties to the White House — she visited more than 30 times — yet adamantly defended herself for nearly 24 hours before finally apologizing as the heat kept building.

The way the president, First Lady Michelle Obama and the re-election team ran from Rosen showed the seriousness of the error.

It reinforces the image of elitism among Democrats and gives Romney an opening among working-class women.

As for Clinton, some in her camp say it’s not clear she would say yes even if Obama came begging.

They say she doesn’t want to be vice president and doesn’t see how running on his ticket would help her win the Oval Office in 2016.

Good points — up to a point. But if Obama needs her, she has little choice. If she says no and he loses, she’ll be blamed. If she says no and he wins, he will owe her nothing in 2016.

All he has to do his beg. The odds are growing he will.

Michael Goodwin is a Fox News contributor and New York Post columnist. To continue reading his column on other topics including President Obama, click here.