The New York Times believes the most interesting data coming out of the latest CBS News/New York Times poll is that the vast majority of Americans think President Obama’s endorsement of gay marriage last week was a cynical ploy to gain a political advantage. That’s the lede in their story about the poll. Considering that the mainstream media — including the Times — gave the statement laudatory coverage, it is surprising to learn that 67 percent of Americans think he did it “mostly for political reasons” rather than believing his story about him evolving and doing what was right. But there’s far worse news for the president in this survey than just the fact that after a few years in office two thirds of the electorate see through him like a sheet glass window. The really bad news is that his core election strategy of seeking to portray the Republicans and Mitt Romney as the enemies of women is not only failing to give him an advantage; it’s backfiring.

The poll shows Romney winning a head-to-head match up with the president by a margin of 46-43 percent. That is interesting, as it’s the first time since early January that Romney is beating Obama in this poll. But of even greater significance is that Romney leads the president among women by 46-44 percent. Only a month ago, Obama had a 49-43 percent edge among women. That this result would come after a month in which the Democrats have pounded Romney and the GOP and sought to portray them as waging a Republican war on women is astonishing. The war theme is apparently not convincing wavering females that a President Romney would harm them. Indeed, it may be having the opposite effect as — just as is the case with the gay marriage issue — many women seem to understand that the war tactic is a dishonest attempt to divert their attention from the more pressing issues relating to the economy.

Like last week’s Gallup poll, the CBS/Times survey also shows that the gay marriage decision is likely to cost the president some support. More voters say they are less likely to vote for the president as a result of his statement than those who say they are more likely to back him by a 22 to 14 percent margin.

Not all the results in the CBS/Times poll were unfavorable to the president. His job approval figure of 50 percent was the highest in two years other than the month Osama bin Laden was killed. And there is more optimism about the economy, with 36 percent saying they think it is getting better, a number that is also the highest in two years.

And yet despite the sense that the economy is not as bad as it has been, Obama is still losing to Romney and even losing among women, a group that has skewed heavily to the Democrats in the past two decades. What can account for this declining gender gap after a period when the president and his campaign have sought to emphasize the difference between the two parties on what they think are women’s issues?

The answer isn’t all that complicated. Though some liberals may be convinced there is a GOP war on women, most aren’t buying it any more than they believe the president’s flip-flop on gays was a principled stand. Whatever their positions on social issues, most women seem to believe that the economy and the well-being of their families is their primary concern and on that score, Obama has lost their confidence. And it’s not clear that it can be won back by ginning up fake controversies that are transparent attempts to demonize Obama’s opponents.

Even more to the point, after three and a half years in office, President Obama may have just worn out his welcome with many voters. Having made it to the White House as part of symbolic election in which all Americans could take pride in righting some great historic wrongs, there is no such rationale for his re-election. Tactics that seem to be merely a way to trick the voters into thinking ill of the GOP are falling flat. The poll may be a wake up call to the Democrats to drop their phony war on women and start concentrating on the bread and butter issue of the economy, which 62 percent of those surveyed say is the most important in the election (the second most is the federal deficit at only 11 percent) where Romney seems to have a strong advantage.