It’s not secret that the United States of America already loves Claire Underwood. She’s frequently by Frank’s side during the campaign, acting as a crucial and supporting figure for the presidential candidate. She’s frequently greeted with uproarious applause and cheers, and she’s too smart to be oblivious to it. In Season 4, we may see her use this popularity to her advantage, whether simply by creating a gaping hole in Frank’s campaign, directly using her followers to slander Frank, or even stealing some followers for her own possible campaign.
Claire seems to be less and less committed to Frank’s image. She was reckless when handling the Michael Corrigan issue even though she knew how crucial it was to his Presidency. How likely is it that she didn't notice someone stealing her scarf while she was asleep? On top of that, she was reckless enough to grab the mic and make an impromptu speech when it was not her place to, ultimately damaging Frank's reputation. Claire is too smart and calculating to allow her emotions to get the better of her. This must have been a subconscious disregard for the consequences, or a deliberate attempt to mess with Frank. Even if Claire actually couldn't control herself, this would show how emotionally unstable she had become, no longer the calm and cool self she once was. Emotions can only be suppressed for so long until, like soda in a bottle, it explodes in a torrent of anger and revenge.
Claire has been passed over again and again for far too long, and she is not the type of person to take all of it lying down. She has been continually denied positions and accused of only getting where she is because of her relation to Frank. She is, and always has been, simply an accessory to his public life, his Presidency, and his campaign. Claire Underwood is not the type of woman to sit back and enjoy being number 2 for her entire life. Frank tells her it’s always been this way, and that she’s always known this, but something seems to have snapped. Perhaps she doesn’t believe Frank can become president anymore, or perhaps she just can no longer stand the idea of only ever being number 2. Either way, she has abandoned Frank, and will no doubt find another more efficient route to greatness, most likely her own campaign, or possibly joining Heather Dunbar on the ticket.
Claire has already been quite popular (and unpopular) with the nation over her abortion and affair scandals. She’s been featured on many news channels and been interviewed several times. However, no publicity is bad publicity. Claire’s name is now out there — and people know her. All she has to do is get those who support her to continue to support her, and get those who don’t, to keep talking about her. She seems to be reveling in the spotlight and building her popularity and name to possibly use in a future campaign. After all, Donald Trump has been getting a lot of hate, but is still doing quite well for himself.
At the end of a Season full of twists and turns, of disaster and recovery, Claire ultimately stands up to Frank. She says to him, “It’s you that’s not enough.” We as viewers assume she’s talking about him in the sense of their marriage — that Frank is no longer “man” enough or able to support Claire emotionally and sexually. However, it could be that the writers decided to include a third layer in this line — a layer insinuating that Frank Underwood does not have what it takes to be President of the United States. Is Claire suggesting something that she knows about the future, that Frank doesn’t?
Claire is Ruthless. We've seen her do things that would make a lot of our stomachs turn. We've seen her do things for power, to help Frank get to the presidency, that would be unfathomable for most wives. She condoned the murder of Zoe Barnes and she condoned the manipulation of most of Washington. No one would put it past her to run against her own husband. In fact, after being pushed down for so long by him, he is the exact person she would want to lash out at the moment she decided to abandon him and his plan to the White House.