By Max Deveson
BBC News, Washington
Bill Clinton has ruled out taking on his wife's senate seat
There are plenty of jobs going in American politics at the moment.
Barack Obama's victory in the presidential election means that his Illinois senate seat now lies vacant.
His running mate Joe Biden's Delaware senate seat is also up for grabs.
And the announcement of his proposed cabinet choices leave a number of other senate and gubernatorial vacancies.
How these positions get filled differs from job to job and state to state.
In some cases, Democrats will even be automatically replaced with Republicans.
In others, the replacement will be appointed by just one powerful individual.
Take, for example, the New York senate seat being vacated by Hillary Clinton, who is now set to serve as Mr Obama's top diplomat.
The 17th amendment of the US constitution sets out the ground rules for replacing senators who resign, die or are expelled.
It allows state legislatures to empower state governors to appoint temporary replacements until such time as a special election can be held.
In many states, however, it can take up to two years for a special election to be scheduled, which means that whoever the governor appoints can sit in the Senate for a considerable length of time.
In New York, the decision as to who will fill in for Mrs Clinton until 2010, when the special election is to be held, will be taken by her fellow Democrat, Governor David Paterson.
New York Governor David Paterson will pick Mrs Clinton's replacement
Names under consideration include the state's attorney general Andrew Cuomo, Nassau County chief executive Thomas Suozzi, as well as a number of New York congressmen and congresswomen.
Caroline Kennedy - daughter of the late president John F Kennedy - has also been mentioned as a possible replacement, but her cousin Robert F Kennedy has ruled himself out, as has Mrs Clinton's husband, former President Bill Clinton.
"In order to appoint the best possible candidate to replace Senator Clinton, I am consulting with a wide variety of individuals from all across New York State," said Mr Paterson, in a statement.
Whoever gets picked will have the advantage of incumbency when the time comes for voters to decide for themselves who should represent them in the Senate, so there is plenty of competition for Governor Paterson's favour.
Similarly, in Illinois, candidates to replace Barack Obama will be hoping to impress the state's governor Rod Blagojevich, who will decide on Mr Obama's temporary successor.
Possible contenders include Illinois congressman Jesse Jackson Jr (son of the famous civil rights campaigner), and Tammy Duckworth, a veteran of the Iraq war who heads the Illinois Department of Veteran Affairs.
In Delaware, Governor Ruth Ann Minner has already declared her intention to replace Joe Biden with Mr Biden's long-time senate aide, Ted Kaufman.
There had been speculation that Mr Biden was keen for his son Beau, (who is Delaware's attorney general), to take his seat, but the younger Mr Biden - who is currently serving as a reservist in Iraq - ruled himself out of the running.
Beau Biden may still run for the seat in the 2010 special election, so having a Biden loyalist like Mr Kaufman (rather than a potential rival) keeping the seat warm until then might prove beneficial for him in the long run.
Governor Napolitano (left) will be succeeded by Republican Jan Brewer
Governor Minner, like Governor Paterson and Governor Blagojevich all belong to the same party as the senator they are charged with replacing.
But if they belonged to a different party, there would be nothing stopping them from appointing a replacement more in line with their own political beliefs (although the states of Alaska, Hawaii and Arizona all require that the replacement come from the same political party as the outgoing senator).
If Democrat John Kerry had won the 2004 presidential election and subsequently resigned his Massachusetts senate seat, his replacement would have been selected by a Republican - the state's then-governor, Mitt Romney.
Although most states give the governor to pick a replacement, some require a special election immediately, so that voters can pick a new senator.
It is not just senate vacancies being opened up by the Obama victory.
He has also decided to pick a number of governors to serve in his cabinet, and his appointment of Arizona's Governor Janet Napolitano in particular is causing headaches for her fellow Democrats in the Grand Canyon state.
In most states, when a governor resigns, dies or is removed, he or she is replaced by the state's Lieutenant Governor, who is an official elected separately from the governor, and can be a member of a different party from the governor.
In Arizona, there is no such position as Lieutenant Governor, and when Ms Napolitano resigns her seat to become Mr Obama's Homeland Security chief, the governorship will pass - by state law - to Arizona Secretary of State Jan Brewer - a Republican.
Unsurprisingly, Arizona Democrats are unhappy about this, not just because they will be losing control of the governor's mansion, but also because Ms Napolitano and her veto were the only things stopping Arizona's Republican-dominated legislature from getting its agenda passed.
"It's a dreadful step," Phil Lopes, Democratic minority leader in the Arizona state house, told the New Republic magazine.
"There is very serious potential of us backsliding on things we Democrats and the residents of the state think are important... I do wish that she would [stay] because with us in the minority chambers, she's the only one who can put a stop to [the Republicans]."
If, as seems likely, Mr Obama picks New Mexico Governor Bill Richardson as his Commerce Secretary, the party will not face similar difficulties, because New Mexico's Lieutenant Governor is also a Democrat.
Mr Obama may appear to have the whole of America's Democratic Party elite at his disposal when choosing his cabinet secretaries and closest advisers.
But the elected officials he picks could leave gaping political holes behind them.
And the governors with the job of picking their replacements will be given the power to make or break political careers.