Anger on the streets at the way the country is run
The leader of the Argentine Senate, Ramon Puerta, is expected to be sworn in as caretaker president on Friday following the resignation of Fernando de la Rua.
He faces tough choices.
The first decision he has to make is whether to try to put together an interim government which would serve out the two years remaining of Mr de la Rua's mandate, or to call elections in the next few months.
Mr Puerta is a leading figure in the Peronist party, which dominates both houses of Congress and most of Argentina's provincial governments.
Many Peronists favour a snap election, in the hope that they will benefit from popular disillusion with Mr de la Rua's Radical party, their main political rivals.
Others within the Peronist party think it would be wiser to wait until 2003, the scheduled date for presidential elections.
They argue that whoever governs over the next few months will have to take some very unpopular decisions - whether to end the parity of the Argentine peso with the US dollar, and whether to default on payments on the country's foreign debt, thereby declaring it bankrupt in the eyes of the world.
This, many leading Peronists say, ought to be done by a short-term caretaker administration, which would bear the brunt of any further popular unrest at these decisions.
Menem
This is thought to be the position of another key political player in Argentina.
He is former president Carlos Menem, who ruled the country from 1989 to 1999.
Mr Menem tried to change the constitution to enable him to stand for a third consecutive term in office in those elections - which Mr de la Rua eventually won - and it is not clear whether he would be eligible to stand again if there was another election now.
Mr Menem has also only just been released from house arrest after allegations of his involvement in illegal arms deals, and would like to use the two years to rebuild his reputation.
Another possible presidential candidate, who would be more likely to want to take over as soon as possible, is Eduardo Duhalde.
He was the Peronist candidate in the 1999 elections, and wields considerable power among provincial Peronists and the trade unions, which are Peronist-run.
Populism
He might win considerable support for a more populist approach to Argentina's economic woes by putting in place measures to help the unemployed, state sector workers who have not been paid for several months, and old age pensioners.
Another figure who could be in line for the position of caretaker president is the man who until a year ago was Mr de la Rua's vice-president.
He is Carlos 'Chacho' Alvarez, who supported the Radicals in 1999, but left office because he felt the De la Rua administration was not doing enough to help improve social conditions in the country.
Mr Alvarez was originally a Peronist, and some local observers feel he could - in the short-term at least - pull the different political factions together in a government of national unity.
A voice conspicuously absent in the current chaos is that of the armed forces.
This is largely because following their military defeat in the Falklands in 1983, they have been successfully kept out of politics.
But in Argentina, with its long history of coups, it is never wise to rule out the possibility that there may be some young colonels waiting in the wings for the politicians to make a mess of things.