There is a belief that if women achieved a majority in Congress- to reflect the majority of women in the population- "they wouldn't find themselves in as much gridlock, with as much conflict and partisan grandstanding as their majority-male colleagues." Supporters of this theory site the "Sisterhood in the Senate" phenomenon where the 20 female Senators (regardless of party affiliation) meet regularly for dinner to promote compromise and cooperation.
Women in the Senate gained much public attention and praise when 6 of the 14 Senators that led the compromise ending the government shutdown in October were women. Similarly, in January, women in the Senate claimed that with more women, the fiscal cliff issue would have been solved more easily.
According to Barbara Mikulski (D-MD), the women in the Senate "don't believe in the culture of delay." Heidi Heitkamp (D-ND) agrees: "One of the things we do a bit better is listen. It is about getting people in a room with different life experiences who will look at things a little differently because they're moms, because they're daughters who've been taking care of senior moms, because they have a different life experience than a lot of senior guys in the room."
Still, the notion that women lead or act differently in Senate or in Congress is not supported empirically. The pivotal politics theory, for example, places members of Congress on a linear ideological spectrum and identifies key players at the 3/5 required for cloture, the 2/3 required to override a veto, and the median voter required for a simple majority. The gridlock interval is location in between the veto pivot and the filibuster pivot. Of course, this theory depends on politicians acting rationally and acting in accordance with their own political preferences; it does not take into account gender identity.
The only reason why gender could make a measurable difference in the prevalence of gridlock is if one gender acts more rationally than another. Women may claim to be better compromisers, but I do not believe that this extends to women acting irrationally and voting against their own political preferences or the political preferences of their constituents.
Would more women in politics lead to less gridlock? No. Women do bring different perspectives, and they bring attention to more women's issues, but changing the gender demographics in Congress will not decrease gridlock. Only more moderate pivots would lead to less gridlock. This could be possible with rule changes, such as the newly adopted "nuclear option"- where only a simple majority is required for cloture- and with the election of more moderate candidates in the future.