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--The Senate--
You might think that every state has had all three partisan mixes in the Senate, since the current two parties have existed for 150 and 190 years, respectively, though not in the forms they have now, and their bases have shifted, and every state has voted for both parties at some point. You would be wrong. Hawaii has only ever had the one Republican Senator (Hiram Fong, who ran for President twice with the rather charming slogan "Can't go wrong with Hiram Fong!"), and Kansas has had three Democrats in the Senate (John Martin, William Thompson, and George McGill), but all three served at least a decade apart.
McGill is the only Democrat ever elected by the people of Kansas to the Senate, as Martin was elected by the legislature upon Preston Plumb's death, and Thompson was appointed to fill the vacancy caused by Robert Howell's death. McGill seemed to have taken the loss particularly hard, as he ran for the next available Senate seat from Kansas, and ran for that seat again the next three times it was up. He was the last Democrat to represent Kansas in the Senate, and since 1939 they've always had two Republicans, the longest streak for any state currently running. Vermont has the all-time record, being represented by two Republicans from 1854 to 1974.
To be fair, many states have had all three mixes, some of them very close together. Virginia went from two Republicans (John Warner and George Allen) to one Republican and one Democrat (John Warner and Jim Webb, which gave Democrats a 51-49 majority in the Senate) to two Democrats (Jim Webb and Mark Warner) in two elections. Meanwhile, Pennsylvania went from two Republicans (Arlen Specter and Rick Santorum) to one Republican and one Democrat (Arlen Specter and Bob Casey, Jr.) to two Democrats (Arlen Specter and Bob Casey, Jr.) in one election and one party change, which gave the Democrats 59 seats in the Senate, 60 once Al Franken was seated, but back to 59 when Scott Brown defeated Martha Coakley for the seat formerly held by Ted Kennedy. (Pennsylvania subsequently went back to one Republican and one Democrat when Pat Toomey narrowly beat Joe Sestak for Specter's seat.)
If you think waiting for the outcome of the 2008 Senate race in Minnesota was irritating (in case you haven't heard, Al Franken was sworn in July 7, 2009), try the 1974 New Hampshire race. John Durkin (D) lost to Louis Wyman (R) by 355 votes, then demanded a recount in which he won by 10, then Wyman demanded a recount which he won by 2 votes. Then it really got messy. Durkin took his case to the Senate, which couldn't decide a damn thing, and eventually they had a new election on September 16, which Durkin easily won. Wyman had the last laugh, though, as Durkin was defeated for reelection in 1980, and the seat has remained Republican since, with Attorney General Kelly Ayotte easily beating Representative Paul Hodes to replace Judd Gregg.
Since 1978, the number of states with a divided Senatorial delegation (one of each party) has been decreasing (and it is now at a historical low), from 28 in 1978 to 17 now. Of the 28 purple states in 1978, ten are now red, nine are blue, and nine remain purple. Of the other seven purple states now, five were blue and two were red. I draw no conclusions from this, as Nebraska's blue pair of Robert Kerrey and James Exon in the 1990s were generally to the right of Maine's red pair of Olympia Snowe and Susan Collins of that decade and the succeeding one. It would seem that polarization has increased, but being of a party and holding a certain ideological viewpoint are by no means necessarily equated. Unless you're a modern Republican, in which case you pretty much have people screaming for your blood if you vote for anything supported by any Democrat.
In 1994, Alabama was represented by two Democrats in the Senate: Richard Shelby and Howell Heflin. Heflin retired and was replaced by Jeff Sessions, a Republican, with views little if any different from Heflin and Shelby. Sessions' victory helped make it possible for the GOP to gain control of the Senate 52-48, and subsequently Shelby and Ben Nighthorse Campbell of Colorado changed parties and joined the majority (which later became 53, since Bob Packwood of Oregon resigned and was replaced by Ron Wyden). People think politicians are opportunistic and power-hungry, but party-switching, even in a chamber in which you are currently the minority party, is not common at all.
Party leadership in the House and Senate usually have safe seats, even if they make them safe by sheer force of personality and building networks. Having a party leader lose reelection is a bit like Simon Cowell being fired from American Idol. However, it has happened a few times: Scott Lucas had served in various positions in Illinois politics for years, even heading Truman's Midwest reelection campaign in 1948 (Truman's running mate was Alben Barkley of Kentucky, Majority Leader from 1937 on, who resigned his seat when he was elected VP), helping elect 9 more Democrats to the Senate along the way, but he only got to serve one term as Majority Leader before he lost his seat. Everett Dirksen easily beat Lucas 54-46, with Joe McCarthy's help (about whom more later), and served in the Senate for eighteen years, the last decade of which he spent as Minority Leader. Lucas' successor, serving as Minority Leader, Ernest MacFarland of Arizona, was himself defeated two years later by Barry Goldwater, and Lyndon Johnson led the Democrats for the next eight years, managing to regain the majority in two. Decades later, John Thune beat the sitting Minority Leader, Tom Daschle of South Dakota in 2004; four years after that, Mitch McConnell narrowly won reelection and felt the need to hold a press conference about it.