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Susan Carroll, senior scholar at the Center for American Women and Politics at Rutgers University, attributes the reversal of the gender gap to faulty polling.

“I have an easy explanation: There is something wrong with the exit poll in Colorado or the way the results were reported,” Ms. Carroll said in an email.

Joe Lenski, executive vice president for Edison Research in Somerville, N.J., said he stood by the results. Edison has been the sole provider of election exit polling to the major news networks since 2003.

Nationwide, Mr. Obama lost a small percentage of the female vote from 2008. Against Mr. McCain, Mr. Obama had a 14 percentage point advantage, but that dipped to 12 percentage points against Mr. Romney, according to a Gallup Poll analysis.

Although Colorado may have been an outlier, Mr. Obama’s strong performance with women was a key to his electoral win.

In Ohio, perhaps the most heavily contested swing state, Mr. Obama carried the female vote by 12 percentage points. Reflecting a pattern in many states, Mr. Romney won among men in New Hampshire by 4 percentage points but lost the female vote in the state by a 58 percent to 42 percent margin.

Colorado Republicans also avoided campaign trail gaffes over such hot-button social issues as rape and abortion that helped torpedo the hopes of Republican candidates in Missouri and Indiana.

Ms. Owens said the challenge now for Colorado Republican women is to maintain their network in a non-election year in order to be ready for 2014.

“Now that we have it going, I want to keep it alive so that we don’t have to rebuild it again,” she said. “We need to keep these connections so that we don’t have to start from scratch.”