The bill is set to be debated in the Riksdag on Tuesday afternoon but by late morning the Centre Party had not yet received assurances that all members of its parliamentary group would vote to pass the bill into law.
"We have adjourned for a little pause but we are in agreement that we should hold the group and the Alliance together," said parliamentary group leader Roger Tiefensee after a two-hour meeting. The meeting was necessitated by the group's failure to hammer out a deal on Monday evening.
One of the Centre Party's most vocal critics of the proposed legislation, Annie Johansson, said she had decided how she would vote.
"I will explain my standpoint in the chamber this afternoon," she said.
Fellow critic Fredrick Federley is also scheduled to speak as part of the debate that will precede Wedneday morning's vote.
The Liberal Party's parliamentary group also held a meeting on Tuesday morning, with Birgitta Ohlsson and Cecilia Wikström indicating the might side with the opposition and vote against the government's proposal.
Frida Johansson Metso, the head of the party's youth wing (LUF), said Wikström had outlined her position in a meeting with LUF.