It's kind of ironic since President Donald Trump tries to belittle Shaheen's colleague Sen. Elizabeth Warren of Massachusetts by calling her Pocahontas -- because Warren once claimed Native American heritage.
"It's kind of a sensitive topic," Shaheen replied. "So probably not."
Warren and Shaheen are two of 21 women now in the Senate. When I first started covering the Senate in 1998, there were only nine.
Still, even when there were only two or three, the women of the Senate have had a bipartisan sisterhood that was nurtured by Sen. Barbara Mikulski of Maryland, who retired from Congress last year but is still known as the dean of the Senate women. The Democrat worked with then-Sen. Kay Bailey Hutchison (R-Texas) to make sure the female senators held a monthly off-the-record dinner.
"We have all really benefited from the efforts of Kay Bailey Hutchison and Barbara Mikulski. Because they started this dinner club ... where they got the women in the Senate together on a regular basis, Republicans and Democrats, to get to know each other," Shaheen said.The dinners -- where, I am told, wine is always served -- are about sharing experiences and getting to know one another on a personal level. As a result, several pieces of bipartisan legislation were born.
"I think the best example during my time here has been the Violence Against Women Act. When we finally got all of the women senators on as co-sponsors, that's when the legislation moved," Shaheen recalled.
Twenty-one may seem like a lot of female senators to serve at once, considering there have only been 50 female senators in all of American history. But it is still only 21% of the Senate, and women make up more than 50% of the population.
"If we continued at the same rate that we had been electing women to Congress, it will take us 100 years to reach parity. So I'm not willing to wait that long," Shaheen said. "We need to get young people excited about politics, excited about government."
To her grandkids, she is 'Govie'
For Shaheen, teaching the next generations starts with her own family. Her oldest daughter, Stefany, was on the city council in Portsmouth, New Hampshire. When she decided not to run again, there was talk of her running for higher office, but she decided not to do it. Shaheen says she expects her daughter to run again when her children are a bit older.
Shaheen's family of three daughters has grown to include seven grandchildren. While many grandmothers are called grandma, nana or meemaw, Shaheen's grandkids call her "Govie."
"I was governor when my first grandchild was born, Ellie, who is now 17," Shaheen explained. "My daughters decided that Govie was something better to call me, and it stuck."Back home in New Hampshire, CNN cameras watched Shaheen engage with and encourage young people.
She approached a group of college students at her favorite diner, Young's, in Durham, and was excited to hear one of the young women there was running for student government.
She offered advice I have heard from other barrier-breaking Senate women like Dianne Feinstein
, which is to start at the local level.
"We have literally thousands of positions in this country at the local and county levels that go unfilled because people won't run for them, and it's a great way to learn," she told the students at the table as they hung on her every word.
"For me, getting young people engaged in politics and public service is really one of the most fun things that I get to do," she later told us.
"Democracy only works as well as those who participate, and if young people are turned off, then it's not going to be good for the next generation."