Underwood is already unpopular with the public; when he's made vice president, the media talks about what a lame pick he is. He's not popular with politicians, either -- he's constantly pissing people off and irrevocably burning bridges to get what he wants, but in politics, you still need people to be willing to take your side when you want to push your agenda through. The fact that he manages to get anything done despite being the biggest pariah on Capitol Hill has been called the most unrealistic part of the show, and this is taking into consideration the scene wherein he murders a woman in public.
Other parts are spot on, though.
So, is Frank just Skeletor, then, in that he became president just because he wants the power? That doesn't make any sense. Frank has been in politics for decades; he has to know by now that the president really isn't as powerful as everyone thinks. Sure, he has influence over a very wide spectrum of issues, but his control over any particular thing is not very significant; often, a group of judges nobody has ever heard of will have more sway over an individual law than he will. Basically, his job is to try to convince other politicians to do the things he wants, which means he needs to be well-respected, and we've already established that this is the one thing that Frank Underwood is not and has no interest in being. But hey, at least he has the relatively poor salary, the complete lack of privacy, and the millions of people cursing his name every day for every inconvenience, no matter how minor, that comes with the presidency.
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Basically, Underwood is like a shitty version of Iago -- he fought tooth and nail to bring the president down out of pure spite, but now that he's become president himself, he's actually made his own life incredibly worse. He busted into the White House like a wrecking ball, but now he's just kind of awkwardly dangling there, waiting to be taken down. If he isn't impeached for his numerous crimes, he'll probably sit around in the West Wing, take credit for any economic upswings for a few years, then make a few bucks on his ghostwritten biography and some graduation speeches at shitty technical institutes.