May I state the obvious? The Herman Cain campaign for the Republican nomination for president is running out of gas. Sure, he’s still topping some polls. The New York Times/CBS News poll released Friday puts him up at the top (18 percent) of a three-way race with Mitt Romney and Newt Gingrich. Both earned the support of 15 percent of Republican primary voters. It should be noted that “undecided/don’t know” actually came in second with 17 percent. But that same poll shows the first concrete sign of trouble for the former capo of Godfather’s Pizza from a key demographic group: women.

Gloria Cain, the embattled candidate’s wife, told Greta Van Susteren in an interview that is scheduled to air tonight on Fox News Channel that her husband “totally respects women.” Well, their respect or fondness for him is diminishing. The NYT-CBS News survey was conducted last week just as Sharon Bialek emerged to put a face on the numerous allegations of sexual harassment against Cain. Sixty-one percent of respondents said the accusations against Cain “won’t make any difference in their vote.” Thirty percent said the charges “make them less likely to back him.” But among women that latter number is 38 percent. And since last month’s NYT-CBS News poll, Cain’s support among women has dropped from 28 percent to 15 percent.

If he’s having this kind of trouble with Republican women helping to decide who will be their party’s nominee, he’s doomed with the dames who will help decide who will be their nation’s next president.

In “Demographic Change and the Future of the Parties,” Ruy Teixeira of the Center for American Progress spells out the advantage Democrats have over Republicans in snagging the votes of women.

Democrats also generally do better among women than men, and they do particularly well among growing female subgroups such as the unmarried and the college-educated. Seventy percent of unmarried women voted for Obama, and an estimated 65 percent of college-educated women supported him. Unmarried women are now 47 percent, or almost half, of adult women, up from 38 percent in 1970, and college-educated women are an especially rapidly growing population. Their numbers have more than have tripled in recent decades, from just 8 percent of the 25-and-older female population in 1970 to 28 percent today.

President Obama ran away with the women’s vote in the 2008 election. While Republican rival Sen. John McCain (Ariz.) got 43 percent of their vote, Obama got 56 percent. According to an analysis of exit poll data by the Center for American Women and Politics at Rutgers University, Obama did better and McCain did worse than the nominees of their respective parties in the previous election. Sen. John Kerry (D-Mass.) won 51 percent of the women’s vote, five points less than Obama would earn four years later. President George W. Bush won 48 percent of the women’s vote in 2004, five points more than McCain.

Then there were these interesting statistics about the 2008 elections from the Pew Research Center. “Nearly 10 million more women voted than men,” according to “Dissecting the 2008 Electorate: Most Diverse in U.S. History.” Women voted at a higher rate than men, 65.7 percent to 61.5 percent. And here’s a killer factoid. “Overall, for the first time,” the Pew report states, “black female eligible voters cast ballots at the highest rate among all voters.” Translation: 68.8 percent of black women who could vote did.

Given the sexual harassment allegations against Cain, his falling support among women in the GOP, the traditional advantage Democrats have with women voters over Republicans and the unlikely event that African Americans (95 percent of whom voted for Obama in 2008) will follow Cain’s lead and leave “the Democrat plantation” in the general election in 2012, I’m pretty sure he won’t be the nominee of his party or president of the United States.