Mitt Romney has a gender gap problem. He's trailing by 19 points among women voters according to our latest poll, so it must be tempting for him to think about picking a female vice presidential nominee.

Senator John McCain tried it when he named Sarah Palin as his running mate. But Republicans I've spoken with have said the 2008 Palin experience makes picking a woman this time around a non-starter.

But it's clear that this so-called "war on women" is going to play a part in the 2012 narrative, so let's look at the women Romney might consider.

There are two impressive and smart governors from South Carolina and New Mexico, Nikki Haley and Susana Martinez. Martinez could also help Romney with the Hispanic vote.

But both women are in their first term and have been convincing in their denials that they do not want to be considered for Vice President - denials that are beyond the normal coy talk of someone who wants to be in the running for VP.

Haley told me on GMA she "would not accept" a running mate offer because she "made a promise to the people in my state and I intend to keep that promise."

Other possibilities are Senators Kay Bailey Hutchison or Kelly Ayotte. Ayotte, from New Hampshire, has a strong past as a prosecutor and a bright future in the Republican Party. But again, she's in her first term and that cuts against her. And it doesn't make much sense for a nominee from Massachusetts to pick a running mate from New Hampshire.

2012 will be Hutchison's last year in the Senate, and there are no other women in top GOP leadership positions in either the House or the Senate.

Romney could also turn to the private sector and pick a corporate titan such as Meg Whitman or Carly Fiorina. But they ran for office and lost in 2010 and both have had moderate pro-choice positions in the past, which would not help Romney court the conservative wing of the party.

If you think I missed any potential women running mates CLICK HERE to send me your suggestion on my Facebook page.

My Bottom Line: The only thing we know about the Republican ticket is what Romney has previously said, that he will pick someone who will undeniably be seen as ready to be president on day one. But I do not think Romney will pick a female vice president this time around.

-George Stephanopoulos