The relation that comes to mind is President George H. W. Bush cousin 3 times removed was Supreme Court Justice David Davis. Bush's Great Grandfather David Davis Walker was cousins with Justice David Davis. Justice Davis is an interesting fellow. He was Abraham Lincoln's campaign manager for the 1860 election. President Lincoln appointed him to the Supreme Court. In the controversy regarding the Election of 1876 Justice Davis was picked as the swing vote to decide how to allocate 20 contested electoral votes. Davis was selected by his colleagues as the swing vote because he was widely considered to be politically Independent towards both candidates.
The Democrats in the Illinois Legislature tried to persuade Davis' vote by electing him as their US Senator. Instead Davis immediately resigned from the court to take the Senate seat. Davis was replaced by a Republican and the Republican Rutherford B. Hayes ended up taking the election by one electoral vote.