"We are dissatisfied with the decision, and we have been all along. Normally such a big change in a social insurance system would have been referred for three months' consideration and an inquiry," said the Social Democrats' Sven-Erik Östberg.
The opposition has been fiercely critical of the decision to increase unemployment fund charges and to reduce payments.
When the decision was due to be made last week the matter was referred back to the labour market committee after a heated debate in which the government was accused of being sloppy in its preparations. The vote was finally taken the following day.
Östberg, who is the vice chairman of the labour market committee and a former temporary finance minister, claims that only one week was made available for submitting views on the proposal. Apart from that, there was just one meeting at Rosenbad, at which the government met union organisations and other interested parties.
"We think that is inadequate," he said.
The Left Party has previously reported the government for what it regarded as being too short a consideration period.
The role of the Constitution Committee is to determine whether or not the government has made a procedural error, and Österberg emphasised that the Social Democrats do not know if any law has been broken.
"From a purely legal standpoint, I don't know what this means. That's why we have reported it to the Committee to have a look at it," said Österberg.
"This hits the low-income very hard, and women especially so. Women working part time could be at risk of not having any unemployment benefit if they lose their jobs," Österberg told TT.
He added that the conservative government was trying to strike a blow against the unions.
"They speak warmly of the participants in the labour market, but things have got harder for one group of participants," he said.
Dagens Nyheter has reported that the Swedish Confederation for Professional Employees (TCO) is looking for cases in its various unemployment funds of part time women who do not qualify for unemployment benefits.
When an appropriate case is found, TCO will push it through the Swedish legal system and ultimately to the European Court, wrote the paper.