The centre-right alliance parties, along with the Sweden Democrats, previously held that the municipalities themselves should be allowed to determine how many refugees they can handle. Now, after the Liberal Party's U-turn, the balance has shifted in favour of the line taken by the centre-left, Social Democrat-Green Party government.
Liberal Party integration policy spokesperson Fredrik Malm tells Radio Sweden that the refugee situation has changed and that has prompted his party to take a new stance.
"The system that we have had now for eight to ten years functioned quite well when the number of refugees coming to Sweden seeking asylum was smaller. Now the numbers are so big. The municipalities agree in January every year on the number of people they will take in, but then in the autumn, they do not meet those numbers. So in the end, the government and the Migration Agency need to have the right to force a municipality to take its responsibility and provide rooms for refugees."
"In Europe, some countries like Sweden and Germany take their responsibility on the refugee and migrant issue while others do not. We have the same situation in Sweden, where some of our local municipalities take a big responsibility while others do not."
Liberal Party leader Jan Björklund told news agency TT that Sweden's stance that other EU members should take their responsibility, should be mirrored at home.
"In the same way that we from the Swedish side now require that all European countries should be involved and take responsibility, and that no one should be able to refuse, so it is reasonable that the same principle also applies at home," Björklund said.
Björklund also told TT: "Some municipalities are saying that they cannot take in a single one - that's something I don't accept."
The government's labour market minister, Ylva Johansson, said she was "surprised" by the Liberal Party's change of heart and told TT that she hopes other parties will follow suit. She said that she can see the government proposal now being adopted in parliament.
"I have always counted on it actually, because I think there is a serious will of the legitimate parties in parliament to work together to cope with a difficult situation when very many people are coming at the same time to Sweden, fleeing war," Johansson told TT.
Minister for Migration, Morgan Johansson, told TV4 News that there is no set time frame yet for the proposal to be put before parliament, which resumes next week.
Under the proposal, the municipalities will, from July 1st 2016, be forced to accept a certain number of new arrivals who hold residence permits.
This evening, Prime Minister Stefan Löfven will meet with all parliamentary party leaders, except the Sweden Democrats' Jimmie Åkesson, to discuss Sweden's stance on the refugee crisis.