New rounds of talks will then increase pressure on the Centre and Liberal Parties to show their true colours.
It has taken seven weeks since Prime Minister Stefan Löfven was voted out as Prime Minister and now the government-building process is coming to a crunch.
After weeks of endless negotiations and press conferences as repetitive as Dinner for One [a 1963 English comedy sketch shown every New Year in Sweden], the parliament now on Wednesday morning has a chance to take a position on a possible prime minister.
It will in all likelihood be a historic vote: It has never happened before in modern times that a prime ministerial candidate has been voted down by the parliament.
On Monday, Ulf Kristersson is scheduled to officially inform the parliaments speaker Andreas Norlén about which political parties will join him in his proposed government.
After this, at 10.30am, the speaker will formally propose Kristersson as Prime Minister. The proposal will be tabled in the parliament on Monday and again on Tuesday, before the vote takes place at 9am on Wednesday morning.
Under Swedens system of negative parliamentarism, Ulf Kristersson does not need to receive a single vote in his favour to become Prime Minister. Instead, he must ensure that less than 175 members of parliament actively vote against him.
If he does not secure a last-minute deal with either the Liberal Party or the Centre Party, it currently looks unlikely that he will manage this.
If you assume that all 144 MPs representing the Social Democrats, Left Party, and Green Party will vote against him, then all it requires is for the Centre Party, with its 31 MPs, to join them, and his attempt will fail.
The leaders of both the Centre Party and the Liberal Party (which has 20 MPs) have previously said they will vote no, meaning Kristersson risks receiving as many as 175 no votes.
The Liberal leader Jan Björklund on Friday reaffirmed in a letter to party members that he and his colleagues planned to vote no.
The Centre Party, however, has said that it will not make a formal announcement on its position until the Speaker has formally tabled the proposal.
So there remains a slim chance that the party's leader Annie Lööf, will on Monday change her position.
The Sweden Democrats have also so-far not committed to opening the way for Kristersson, although they are widely expected to either abstain or vote in his favour.
If the Centre Party does abstain or actively vote for Kristersson, he is expected on Thursday to publish a list of the ministers he plans to appoint, after which he will go to Royal Palace to be confirmed as Swedens new leader.
Traditionally, the new government will then be photographed at Lejonbacken, a part of Stockholms Old Town, just in front of the Royal Palace, after which the ministers will go to be greeted at their various departments.
If, as is more likely, Kristerssons attempt falls, then the Speaker will begin a new round of talks, after which he is expected to propose a new prime minister candidate.
That could be Social Democrat leader Stefan Löfven, but it could also be Annie Lööf, leader of the Centre Party, who could try to piece together a centrist government with the Green Party and some of her Alliance partners, relying on the Social Democrats for support.
If this route is tested and also fails, Lööf and Björklund may then be more open to backing Kristersson in a future round.
Up until now, they have tended to say “not for now”, or “not in the current circumstances” to Kristerssons proposed minority government, which indicates that they are leaving themselves room to change position later in the process.
“If all other reasonable alternatives have been tested to the full and still dont work, we do not rule out Sweden in the end having a right-wing government,” Björklund said to TT earlier this week.
The Speaker can make four proposals for Prime Minister, after which, if none are accepted, a new general election will called.
The Centre Party and the Liberal Party will sooner or later be forced to show their cards: are the ready to think again about their no, or will they begin negotiations over the political dividing line as individual parties?
This analysis is an adapted translation of an analysis article by TT's political reporter Owe Nilsson.