Winning the female vote is challenging for any Republican. Women have traditionally identified strongly with the Democratic Party, while male voters are split between the two parties.Obama won the popular vote by 4 points. Female Obama voters only did 8 (= 12 - 4) points better than that, while male Obama voters did 12 (= 8 + 4) points worse.
The largest gender gap ever was recorded in the 2012 presidential election: 20 percentage points, according to Gallup. Mitt Romney won among men by 8 percentage points while President Obama won women by 12 percentage points over all. But among white women, Mr. Obama lost with just 42 percent to Mr. Romney’s 56 percent.
So women identify Democrat only about as much as men identify Republican. To the extent that Republican have trouble getting women to vote for them, Democrats have trouble getting men.
As the article notes, Republicans did win the white female vote. They also won married women, and Christian women.