There is not a lot of downtime for members of Congress, but some of theirs is spent playing softball to raise money for young women with breast cancer. Ms. Wasserman Schultz is a co-captain for the House on a Congressional women’s softball team, and Ms. Gillibrand serves as a co-captain for the Senate side.

“I don’t think I’d be talking out of school if I told you Kirsten and I are pretty good, and Gabby, not so much,” Ms. Wasserman Schultz said. “We have to really coax her to participate. Let’s just say she was in the process of skill building.”

Ms. Wasserman Schultz, Democrat of Florida, met Ms. Giffords through a legislative fellowship program, before the Arizona lawmaker came to Congress, and she campaigned for her in Tucson, eager to see her join the ranks. Ms. Giffords and Ms. Gillibrand were part of the “red to blue” Democratic Party strategy to get moderate Democrats to take over Republican districts.

Once Ms. Giffords got to Washington, she and Ms. Wasserman Schultz melded their families in leisure time, going to the last shuttle launching or vacationing in Ms. Wasserman Schultz’s home in New Hampshire. “We would go hiking, and our on our boat and cook dinners,” she said. “Mark’s children and my kids played together. It’s just really nice.”

In Congress, party is all, but gender can help. “There is a bond among the women in Congress that goes beyond party,” said Representative Cathy McMorris Rodgers, Republican of Washington, who remembers that women from both parties had a shower for her when her son Cole was born three years ago.

“There are experiences and issues that bond us together, and we understand that we are still deep in the minority in terms of being women,” she said. “We often work together on things that are important to women and children and families, and there is a unique opportunity that we have, being women, to work on these issues together. I think we all recognize it’s still challenging to win a race for Congress, period, and as women, we share a goal of getting more women elected.”

That is not to say that the women were constantly engaged in identity politics.

Ms. Giffords gave Ms. Pelosi, the Democratic leader, a Christmas ornament one year that she has kept. But that did not stop Ms. Giffords from voting against Ms. Pelosi this month when she sought, successfully, to keep her party’s top post.

But the women’s bonds thrive in many ways. Even their softball team is bipartisan, unlike the Congressional men who play against each other by party. “That has given us a nice opportunity to bond across bipartisan lines,” Ms. Wasserman Schultz said. “I think, in general, the women across the aisle are a bit more civil to each other. Maybe we will be the ones that lead by example.”