As he has told us so many times in his Foghorn Leghorn accent, Frank Underwood wants to be the president.
Frank is manipulating and blackmailing and straight up murdering people with the end goal of being president, but why? The position comes as an obvious accessory to his quest for ultimate power, but it's never quite clear what he wants to do with it. People don't strive to be president for the mere sake of being president; they have goals, ideals and policy changes they want to see put into action. That's not to say they need to invoke hope and change. Their motives can be questionable or down right evil. Heck, if Frank wanted to be president solely so that he could use martial law to take over the universe using only sharks with frickin' laser beams attached to their frickin' heads, he'd at least have a reason for wanting to be president.
The actual issues in this most current season are, as Slate notes, refreshingly feminist. Claire Underwood's anti-rape bill, inspired by some falsified though sympathetic claims, is an invigorated glimpse at the war on women, but the way the bill is lobbied for and eventually compromised over is eventually revealed as yet another cog in Frank's president-becoming machine.
Everything has to be about (in some way or another) law-making or policy formation and yet we have little exposure to the basis for any scheming. When there is talk of the House majority's fear of becoming the minority, we almost have to ask ourselves ... wait, is Frank a Democrat or a Republican? That's partly tongue-in-cheek, but his material motives are truly that unclear.
The few issues that are explicitly addressed seemed to be a causal element of plot functionality -- the U.S.-China relations, which fuel Frank's battle with Raymond Tusk, the need to raise the retirement age in order to avoid a government shut down -- but no one seems to truly care about much of anything. That's not to say they seem insincere or malicious (though they do) as much as it's unclear WHY everyone is being so manipulative and strategic in the first place.
Really, it's a comment on the show in general. But our focal point, Frank, is the epitome of substance-less battling. His end goal is to be president, but once he is seated in the Oval Office after having, maybe, pushed the standing president on to some subway tracks, what will he do with the position? Heartless scheming is great entertainment, but only as a means to an end. If Frank finally becomes president, will the show be about anything other than the unraveling of his diabolical past? Aside from fighting for a manipulation bill, it doesn't seem like there's much on his ideological docket.