If the badass women of BSG ruled the world, the country’s problems would be fixed in no time, and I bet you anything their presidential cabinet would look something like this:
President Roslin would prevent the extinction of the American political system by a group of cold, robotic, brainless individuals who call themselves “The Tea Party.” Roslin would never once give in to this so-called Tea Party, even when they occupied the White House front lawn to protest her plan to raise taxes for Americans who have no desire to procreate.
Unfortunately, the President’s secret battle with cancer would be leaked to the press, including revelations that her disease was once cured with the help of a fluid taken from a Hybrid (Prius), leaving American citizens to wonder if this fluid exchange means that President Roslin is now a Hybrid herself, or just so desperate for a cure that she would allow a doctor to inject car juice into her butt?
First Order of Business: Reboot the NASA space program and give it a new mission: to land on a far away planet that President Roslin saw — in one of her hallucinogenic visions — was giving away cheap gas.
Vice President: Boomer (a.k.a Lt. Sharon Valerii) 
It would become evident by the end of President Roslin’s first year in office that VP Boomer is really a sleeper agent for the Republican Party. By the time anyone finds this out, however, Boomer would have already used her tie vote as president of the senate to pass bad fiscal policies that only benefit “Gaius Baltar fund managers,” “tylium fuel companies,” “corporate viper owners,” and “cubit millionaires and billionaires.”
First Order of Business: Be torn between her official loyalties to President Roslin and her secret loyalties to the Republican Party; then go home and be torn between her official loyalties to her family and her secret loyalties to her next door neighbors; and then go to her bedroom and be torn between her official loyalties to her French poodle and her secret loyalties to her daughter’s Siamese cat.
Secretary of Defense/Secretary of State: Starbuck (a.k.a. Kara Thrace) 
Starbuck would not only double as the Secretary of Defense and the Secretary of the State, but she would also triple as the best pilot in the U.S. Airforce.
She would be cocky, would continually challenge President Roslin’s authority, would kick a French ambassador’s ass for no reason except that she didn’t like the way he looked at her, would smoke Cuban cigars despite the U.S. embargo, and then would get Putin to cry after beating him at Triad — twice.
Finally, to everyone’s shock, after Secretary Starbuck secured a long sought-after peace treaty between Israel and Palestine, she wouldn’t come back home to celebrate the victory — she’d just disappear. Leaving the country to wonder whether Secretary Starbuck was just a clone, an angel, a figment of everyone’s imagination, or just another foreign spy out to mindfuck the American intelligence community forever.
First Order of Business: Lead an air strike against terrorists hiding in Afghanistan; then, after a successful mission, get drunk off her ass, frak one of her fellow pilots in the locker room, kick the guy out, then start painting pictures of black holes all over the walls while she laughs and cries at the same time.
Secretary of Labor: Admiral Helena Cain (from Season Two of BSG)
As the Secretary of Labor, Cain would search for every corporate CEO in the country who gave themselves bonuses during the Recession. Once she found them, she’d proceed to torture them with reruns of “Two and a Half Men” until they finally conceded to cut their pay in half and use the extra money to hire more employees.
Unfortunately, things would get bad for Secretary Cain once she ordered one of her assistants to launch a guerrilla attack on companies who tried to break unions.
Cain’s assistant would decline to follow Cain’s order, thinking it an unwise move. Everyone in Cain’s staff would then get really serious, and Secretary Cain would ask her assistant to hand over her iPhone.
After some hesitation, the assistant would hand over her iPhone.
Secretary Cain would take the iPhone, click on the “sawed-off shotgun” app, and then proceed to “shoot” her assistant in the face.
First Order of Business: Take out a real sawed-off shotgun from underneath her desk and this time really shoot her assistant in the face.
