Absolutely not as a matter of history
If the characters of House of Cards are based on the Clintons, then the BBC has access to amazing foresight.
The American series is based on a 1990 BBC original and initially follows the plot closely. Bill Clinton didn't even become president until 1992.
Moreover the plot and character behaviour don't follow the Clinton's path closely (unless you are a believer in some pretty extreme conspiracy theories).
For example, Francis Urquhart (the same character as Frank Underwood in the US series) doesn't initially become prime minister by getting elected but by machiavellian plotting against the existing PM. Frank Underwood follows exactly the same path to the presidency. Bill Clinton, on the other hand, was elected as a somewhat outsider candidate and didn't plot to overthrow his boss and gain the presidency because of some personal slight. Moreover, the lead character's wife in both series encourages her husband's adultery as a means to achieve various goals. It is hard to see how any of Bill Clinton's alleged or demonstrated dalliances has done anything to further Hillary's career nor did they help his own.
The wife-husband relationship involves a strong woman in both series who supports or eggs on her husband's nefarious activities. You can read the relationship between Bill and Hillary into this, but it can hardly be based on that relationship since the Clintons were complete unknowns when the original BBC series was aired.
Given the similarity of the US series to the BBC original it seems considerably likely that any intentional mirroring of the Clintons was not intended. You can, of course, read into it whatever you want but the history strongly suggests that no similarity was intended.