Under similar circumstances in 1974, then-Prime Minister Ted Heath resigned on the Monday following an inconclusive Thursday election, after conducting failed coalition talks. Some commentators expect similar timing this year.
A blog on the website of The Daily Telegraph, a London newspaper, give some clues on the timing question:
Lib Dem sources describe Cameron's offer as a "significant step". He will meet with his new parliamentary party tomorrow [Saturday] afternoon.
The first face-to-face talks between the Tories and Lib Dems are due to take place tonight [Friday], after David Cameron and Nick Clegg chatted on the phone earlier, the BBC reports.
The BBC's Nick Robinson predicts that the Browns will be packing their bags and moving out of Downing Street within days after Nick Clegg and David Cameron thrash out a deal over the weekend.
Coalition negotiations in some parliamentary democracies go on for weeks. Because the British rarely face these circumstances, I suppose we can't rule anything out. I suspect that the most likely scenario under which negotiations would be extended over a long period of time, would involve a breakdown in negotiations between the Conservatives and the Liberal Democrats.
It would obviously take additional time, if negotiations had to restart from square one, if Labour then became the Liberal Democrats' interlocutor. Also, Labour-Liberal Democrat negotiations might be more complicated by the fact that, unlike a Conservative-Liberal Democrat alliance, a Labour-Liberal Democrat combination would require at least the tacit support of the nationalist parties outside England, because Labour and the Liberal Democrats do not have enough combined seats to constitute a majority.
Aside from the timing question, there are some interesting quotes on that Telegraph blog about the possible nature of an alliance between the Conservatives and the Liberal Democrats:
Sir John Major, the former Prime Minister, says Tory concessions to the Lib Dems to strike a deal would be a "price worth paying".
William Hague says cabinet jobs for Lib Dems are not off the table. He said "there must be a lot of scope to talk" about the subject of electoral reform between the two parties. He said Cameron has taken the initiative.