I can think of a few decent examples, but none are perfect:

Depending on what view you take Huey Long is a decent candidate. If you take the cynical route he used populism to consolidate almost total political power in Louisiana, serving as both governor and senator. He was eventually assassinated in 1935 on the eve of a potential presidential run.

Boss Tweed is a better example of someone who used outright illegality to achieve political power. He didn't reach Underwood's national prestige, but the Tammany Hall machine maintained control of New York politics until the 1930's. Other Democratic political bosses charted a similar path like James Michael Curley who was elected to the House after serving in prison, and was re-elected mayor of Boston while serving a felony conviction. Like Tweed though he was mostly a local power.

As for Presidents, the only election I can think of that can definitively have been said to have been stolen by scheming is 1876 when the Republicans gained the Presidency in exchange for ending reconstruction, but Rutherford B. Hayes was such a wet blanket of a man that it would be strange to compare him to underwood.

As others have pointed out, LBJ is clearly a model to Underwood, as is TR whose portrait is displayed so prominently. The Indian Casino storyline is ripped straight from the scandals of Tom Delay, and the other big speakers of the past few decades like Tip O'Neill and Newt Gingrich are clearly influences. I'm pretty sure when the Republicans in House of Cards flee the capitol to avoid a quorum and then underwood has them arrested by the House Sergeant at Arms that this is a reference to the Texas 11 and Tom Delay's threat to have them arrested. Some people see the relationship between Claire and Francis as being like that of Bill and Hillary Clinton, who have also been mired in their own fair share of political scandals, and, Francis is, like Bill, a southern democrat. But that conniving relationship with an all-knowing wife is present in the British series, so I doubt that.

The Nixon administration obviously had the best examples of the kind of dirty tactics that underwood uses, but I assume that history is well known, and Underwood doesn't seem very Nixonian to me in anything except his willingness to break the law.

Edit: he wasn't an elected official but Lee Atwater might interest you as an example of American politics at its most cynical.

Frank Underwood is based upon the British version of the character, Francis Urqhart, which in itself is based upon the book. But the writers have also used traits from people like Tom Delay and LBJ.

Source: http://www.gq-magazine.co.uk/entertainment/articles/2013-02/15/house-of-cards-netflix-review

Could you describe the character? Without being familiar with the show it would be difficult to give an answer.