Carly Fiorina greets attendees during the Quad Cities New Ideas Forum in Davenport, Iowa, on Sept. 25. Bloomberg AFP/Getty

Republican women in Congress are thrilled to see Carly Fiorina, a well-spoken conservative female politician, climbing the ranks in the presidential race. But that doesn’t mean they’re backing her.

Though they are excited to see one of their own making waves in the presidential contest, just two so far—Reps. Candice Miller and Lynn Jenkins—have lined up behind her campaign, and it’s unclear whether the former CEO should expect much more support from Capitol Hill in the near future.

Fiorina headed to Washington Wednesday evening to sway more support to her side. She was set to appear at a roundtable discussion for members and staff only, hosted by Rep. Jeff Duncan of South Carolina, at the Capitol Hill Club. Duncan’s staff has emphasized that the event is not an endorsement of Fiorina but one of several events he’s hosting with the 2016 candidates to introduce them to his colleagues.

“I have said for years that the first female president would be a Republican president,” Rep. Marsha Blackburn of Tennessee says, laughing. But is she supporting Fiorina in that effort? No. At least not yet.

While electing the first female president would be thrilling for GOP women, it’s not enough for many of them.

When Miller landed in Cleveland for the Republican debate back in August she heard one name over and over—and to her surprise, it wasn't the name of one of the candidates she'd flown to Ohio to see; it was the name of a woman, a candidate whose polling hadn't even qualified her for the main-stage debate.

“When I arrived, the whole town was talking about Carly Fiorina in the ‘happy hour,’ whatever they called it, the lower-tier [debate],” Miller said. The Republican who has represented Michigan in the House for more than a decade missed the earlier debate in favor of the night’s 12-candidate main event. But by the time the second Republican debate rolled around, Fiorina had earned a spot on the main stage and earned Miller’s attention.

Miller, the vice chair of the House Homeland Security Committee, said that her top two issues in any cycle are the economy and national defense, and, for her, no one on that stage could touch Fiorina. “You know, when she was on that debate stage out in Simi Valley, of course everybody said, ‘Oh, I’m in favor of national defense, strong military.’ Well, of course, we all are. But she started articulating—enumerating really—what we needed to do as far as how many battalions in the Army and what kind of fleets like you see in the Navy and what was necessary,” Miller said.

Miller, now one of Fiorina’s two endorsees on Capitol Hill (both of whom are women), says she is excited to see a woman performing so strongly on the debate stage in a presidential contest. “I think it’s important that women, who are half the population, are represented,” Miller said. But that’s far from the reason she’s endorsing Fiorina.

For Miller, and for many of her female colleagues on Capitol Hill, Fiorina’s gender is “just the icing on the cake.”

Republicans have long dismissed the identity politics that they see as so central to the Democratic Party. Whereas members of the minority talk constantly about Hillary Clinton’s gender, the potential of the first female presidency, and the so-called “women’s issues” that her candidacy brings to the forefront of political discussion, numerous Republican women in Congress dismissed gender as a factor in Fiorina’s candidacy.

Sen. Susan Collins, who is a vehement Jeb Bush supporter, said she is nonetheless excited to see another woman doing so well in the race and is “impressed” by Fiorina, noting that she has “given two outstanding performances in the debate[s].”

Collins pointed out that Fiorina is just one candidate adding to the “amazing diversity” of this year’s Republican field, which features an African-American doctor and two Hispanic senators in addition to “a very capable woman.”

For these women, some of whom have served in Congress for decades, earning their seats long before there was even a women’s bathroom off the House floor, there is a strong sense of concern about tokenism. Blackburn, who noted that she has known Fiorina for years and praised the CEO for “kicking up some dust” in the crowded 2016 field, has not yet made an endorsement in the race. “You know, for any of us who are females working in elective office … I think we want to make certain that it’s not gender; it’s the person who is the most qualified,” she said.

Jenkins, Fiorina’s other endorsee on Capitol Hill, emphasized that she supports “businessperson” Carly Fiorina for president, an outsider who she believes can best help the country, noting that “this was always supposed to be a citizen government."

“I’ve never really considered gender a high priority; I vote for the person, and I think most people do,” Jenkins said in an interview on Thursday. “We’re just hungry for leadership; there’s a leadership vacuum in this world, and we see the leadership potential that Carly has.”

The Kansas Republican dismissed Fiorina’s gender as particularly helpful in a potential general election against Clinton, brushing aside arguments that Fiorina’s own inner circle has made that the former Hewlett Packard executive’s presence in the race could hurt Clinton’s ability to cast the party as antiwoman.

Fiorina’s advantage, Jenkins said, would not be her gender, but her background. “I just think there’s a stark contrast there—the success that Carly’s had and her personal narrative and success in the private sector. And I think that stands in hard contrast to Hillary, who has just had a political career as a politician and a political operative, and her record is largely failed,” Jenkins said.

Miller, for her part, said that she looks forward to a Clinton-Fiorina debate. “In my mind, the best debate would be between Carly Fiorina and Hillary Clinton. I would take that debate all day long. All day long,” Miller said. “I would absolutely love to see that. I mean in my lifetime, if I saw that debate?”

Sen. Shelley Moore Capito of West Virginia said that she too is thrilled to see a woman doing so well on the debate stage, adding: “I think we would love as Republicans to be the first party to elect a woman president. Why wouldn’t that be a great thing?”

But for Capito, and many of her colleagues, when it comes to actually electing the next president, gender is beside the point. "I think the reason Carly is doing as well as she is is because she has incredible knowledge, she does her homework, she works hard,” Capito said. “You know, I think Hillary has probably a lot of the same—does her homework, works hard. So I don’t think it’s the gender; it’s the depth of knowledge.”

Sen. Deb Fischer of Nebraska echoed that feeling, saying that while she is “proud” to see another woman performing so well on the 2016 debate stage, she’ll make a decision in the race based on the qualities of the candidate. “It’ll be a milestone, of course, when the first woman is elected, just as the first African-American, the first Hispanic—that’s always a milestone,” she said. “But I think the American people are always looking for the best-qualified candidate, the  person who has the character, who has the vision, who will truly lead this nation. That’s what I look for in a candidate.”

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