Representative Marsha Blackburn, the Republican of Tennessee who recently advised her own party to put a woman on the ticket in 2016, says that when she's talked down to, or called "sweetie", she tries to deal with it "with humour instead of getting upset" because it is simply a fact of life. "Sometimes it makes men feel good not to treat you as an equal," she said. "I take delight in proving them wrong."
Some conservatives, though, worry that being a woman also gives Clinton an unfair advantage. Wall Street Journal columnist and editorial board member Mary Anastasia O'Grady recently called gender her "biggest asset, for sure, because there are just so many women voters who will vote for her solely for that reason, I'm afraid".
Supporters of Clinton, or any other candidate, for that matter, would surely not see their vote as "solely" awarded on that basis.
In a recent Bloomberg poll, 12 per cent of respondents asked about the idea of electing the first female President said they'd be more inclined to vote for a candidate on that basis, while 4 per cent said they'd be less inclined.
Neda Moyer, a Republican voter in Virginia, says she's been arguing with her Clinton-supporting sister, who is a Democrat, over whether "making history" in the 2016 presidential contest matters: "I don't understand that thinking," said Moyer, an executive assistant in her 50s. "Would it be cool to have a woman in office? Absolutely, but I care a lot more about what you're going to do."
As Clinton begins laying out her plans if elected, what is it like today for her and other women on the stump? Representative Terri Sewell, the Alabama Democrat, recalls interviewing the pioneering New York congresswoman and presidential candidate Shirley Chisholm for her senior Princeton thesis in 1986. When she asked whether it had been harder running as an African American or as a woman, Chisholm said the latter was "unequivocally" more challenging. And in Sewell's own experience, "that's as true today as it was when she told me that 30 years ago".
Kristen Hayes, a children's environmental health advocate who unsuccessfully ran for a seat in the Pennsylvania legislature last year, describes her experience as educational in ways she never expected: "I'd hear, 'Oh, good for you, sweetie'. Or 'I like your hair. I like your necklace'. Or 'You're too pretty to be a Democrat'. Or they'd ask me out - publicly, as I was trying to talk! I was like, 'Seriously? We have no infrastructure and potholes bigger than third-world countries and you're going to ask me if I want to go out'?"
Her biggest hurdle, though, she says, came from women in her own party over her opposition to abortion rights. So, the day after the election, she switched her registration to Republican. It's hard to imagine anyone daring to call Hillary Clinton "sweetie" - and if they did, it would surely backfire. Yet apparently, there is still a market for T-shirts that say, "Iron my shirt!" in honour of the young men who yelled that at Clinton during her last campaign.
Former House Speaker Nancy Pelosi, who has been portrayed in attack ads as a dog, a witch and a monster, says that what she stresses to first-time female candidates is that they have to have enormous confidence in themselves, along with commitment and clarity of purpose: "What I tell women is, 'This is not for the faint of heart ... You have to believe in who you are and what difference you can make ... And that's not to be egotistical, it's just to be confident."
You'll need all of that you can get, even if Republican Carolyn Maloney, the Democrat from New York, thinks things have gotten better for female candidates since her first Congressional run in 1992. Back then, she was described in the New York Times as having the energy of a "puppy dog". And "I think it was meant to be a compliment".
When Hillary Clinton ran for the Senate in 2000, a neighbour of Maloney's told her at one point that he couldn't vote for Clinton because she wasn't strong enough. "Then later this same person said he couldn't vote for her because she was too strong."
At this point, though, Maloney has the sense that "the country is ready" for her friend Hillary Clinton - a feeling that she says comes from "the depth of support among male voters, these macho men coming up and telling me she's the one".
McCaskill's confidence in Clinton's prospects comes from not so much from changes in the electorate as from what she sees as a change in the candidate herself: Under all the scrutiny "it's easy to become a one-dimensional caricature" of oneself in public, she said. But recently, "I've had conversations with her where she appeared to be relaxed and loose - she's trying to be less, quote-unquote, prepared, and more authentic, to let people see she's not this wound-too-tight automaton".
The senator, who herself supported Obama over Clinton in 2008, says "most Americans know it's past time" for a woman in the White House, and feel, too, that "it's very important for young women and girls to hear the words, 'Madam President'."
Still, she says, "they'll vote for the candidate who understands them best," and if that's Hillary Clinton, as she's sure it will be, it's then that history will be made.
Meanwhile, though, the candidate still has to deal with "the double standard about judging a woman by her spouse, when that door doesn't swing the other way". And according to the senator, who has three grown children, four stepchildren and eight grandchildren, the internal pressures change but don't disappear: "I know she's going to have pangs of guilt about not having enough grandma time."
