But actually Republicans continue to have a gender problem that transcends race. While Romney did indeed win with white women (+14 Romney), he won by a far larger margin with white men (+27). So there is still a gender gap among whites. (The gender gap is defined as the difference between men and women's support for a candidate.)
And while the gender gap among whites was a bit smaller in this election than the gender gap among blacks and Latinos, the gender gap among all three groups rose from 2008. The chart below shows the gender gap across race for every presidential election for which we have public exit polls.
Obama's gender gap among whites in this election was lower only than Clinton in 1996 and Gore in 2000. Further, while not on the chart above, the 2012 gender gap among whites was also larger than that in the 2006 and 2010 midterms (3 and 5 points, respectively). To claim the gender problem Republicans faced in 2012 is "merely" a race problem is the denial that has actually helped cement this pattern.