In The Pope Resigns: Why February 11? I speculated that Pope Benedict XVI had made his resignation effective on February 28 in order to provide enough time for a new pope to be elected and installed before Palm Sunday. That would allow the new pope to preside over the celebrations of Holy Week and Easter, liturgically the most demanding of the year.
That hunch seemed confirmed when Pope Benedict issued his final motu proprio, which, among other things, allowed the College of Cardinals to set the date for the conclave to elect a new pope earlier than 15 days after when the Chair of Peter became vacant. The formerly mandatory 15-day waiting period reflected the fact that, normally, the reign of a pope ends with his death rather than his resignation. The 15 days provides enough time for the members of the College of Cardinals to travel to Rome and for the funeral Mass for the previous pope to be held.
Obviously, in the case of Pope Benedict's resignation, a funeral Mass was not necessary. Therefore, it made sense to allow the College of Cardinals to move up the date of the conclave, provided that all of the cardinal-electors—the cardinals under the age of 80 who will be able to take part in the conclave and to cast votes in the election—were present in Rome when that date was set. Setting the date before all the cardinal-electors were present would open up the possibility that one or more cardinal-electors might not arrive in time for the conclave, and so Pope Benedict wisely required all cardinal-electors to be present before a vote on the date could be held.
In the meantime, those cardinals who had already arrived in Rome held a series of meetings, two each day, known as General Congregations. On Thursday, March 7, 2013, the final of the 115 cardinal-electors for the upcoming conclave arrived in Rome. And so, in the ninth General Congregation of the College of Cardinals, held in the evening (Rome time) of Friday, March 8, the cardinals voted to convene the conclave on Tuesday, March 12, 2013.
That's not much of a head start over the mandatory 15-day limit of the past, but in all likelihood, it will lead to the election of a new pope by the end of next week. Since the election of Pope Gregory XVI in 1831, which took 83 ballots over the course of 64 days, no papal conclave has lasted more than five days, and most have taken three days or less.
Pope Benedict himself was elected on the fifth ballot, on the afternoon of the second day of the 2005 conclave, barely 24 hours after it began. While no one expects the 2013 conclave to be that short, it would be surprising if it lasted more than four days.
And that would mean that the new pope would be installed sometime in the week before Palm Sunday (known until the revision of the liturgical calendar in 1969 as Passion Week, the first week of Passiontide, of which Holy Week was the second).
Of course, anything could happen, including a deadlocked conclave that could last longer than the one in 1831, or the election of the new pope on a single ballot on Tuesday afternoon, when the conclave begins. With no obvious consensus candidate, however, the latter scenario is very unlikely, and in this day of modern communications, when television and webcams will be pointed continuously at the chimney of the Sistine Chapel, waiting for smoke, black or white, to emerge, the 115 cardinal-electors will undoubtedly feel pressure to keep their deliberations brief.
Don't expect the announcement to be timed for the 6 o'clock news, though. Even if the cardinal-electors proceed with all deliberate haste, the cry "Habemus Papam!" ("We have a Pope!") will happen when the Holy Spirit wills it. The Church is a worldwide institution that doesn't cater to the need of the American television networks, and if you want to make sure that you see the white smoke and hear the announcement, you'll have to keep one eye on that webcam throughout the proceedings.