Frank himself says that he will win because Claire Underwood is standing by his side. Does this mean that Heather Dunbar would win if Claire were standing by her side? Is he trying to say the only way he can win is because of Claire standing by his side? This may simply be Frank pandering to the audience, but it may also be the writers foreshadowing something a possible loss in the future. Well, Claire is no longer by Frank’s side. Is Claire going to join Dunbar’s ticket? Is she going to run herself?
This is perhaps the strongest case for Claire’s presidential campaign. She is already imagining herself as the President! Frank walks into his own office to see someone sitting in his chair — his own wife. The way Claire faces Frank, an inexperienced viewer could mistake Frank as the First Gentleman and Claire as the President. She fits the chair so naturally and elegantly that it is almost impossible to imagine Claire NOT running for President. This is some of the more blatant foreshadowing done by the writers, and we’ve certainly picked up on it.
Claire Underwood wants freedom. Her entire life has been dedicated to advancing her husband's career, and her life has been put on hold in the meantime. She even is restricted from doing something that she loves and uses to destress -- running. In the final episode of Season 3, Claire has to abandon her passion for running and instead opt to use the rowing machine in her home in fear of being seen outside, and thus conveying to the world that she is not with Frank on his campaign. Something as simple as leaving the house now revolves around Frank's life. Symbolically, she has even adopted Frank's method of exercise, the rowing machine. She hates her new lifestyle, and she hates the root of it (she even says so to Tom), her husband. All this hate is bound to be released after she leaves Frank, whether it be in the form of leaking information, or a direct head to head campaign battle.