Labor has questioned Bob Day's decision to remain in parliament until the end of the year after the Family First senator initially said it would be "untenable" to stay.

The furore comes as Family First revealed it had put Senator Day’s replacement on hold as he had told the party of a “new potential investor” for his housing businesses.

Senator Day, whose Home Australia group is in liquidation with more than 200 houses left unfinished, said on Wednesday he could not resign before the end of the year because the upper house had too much important business to consider.

With just three sitting weeks left, he says there isn’t time to install a replacement for him if he quits to sort out the liquidation.

“Marriage plebiscite legislation, ABCC and our other work too important to Family First to have a vacant seat for even 1 day in November,” the senator tweeted.

Senator Day last week issued a media release in which he stated it would be “untenable to stay in parliament” while trying to do his best to help subcontractors and families put out by the business collapse.

Labor leader Bill Shorten said the situation looked like a deal between Senator Day and the government, which required his vote to pass the Australian Building and Construction Commission bill – one of the two double-dissolution election triggers.

“How is it that one week he thinks his position is untenable, then, when he can’t manipulate his preferred replacement through his political party, he has now decided to keep taking the $4000 a week and support the government’s anti-worker legislation?” Mr Shorten asked reporters in Melbourne.

“It wasn’t Labor who has left hundreds of families high and dry, it wasn’t Labor who said his position was untenable, and Labor is certainly saying this whole situation smells.”

Treasurer Scott Morrison said it was the South Australian senator’s call.

“He makes the decision on when he resigns and when he doesn’t resign,” Mr Morrison told 5AA radio.

The South Australian government has offered to convene a joint sitting of parliament next week if Family First wanted to quickly fill the casual vacancy.

However, Family First’s South Australian leader Dennis Hood said that while the party executive had met last Saturday to determine a possible preselection process to replace Senator Day, the process had been temporarily put on hold.

There had been no discussion of individual nominations, despite reports up to 10 people were interested in the seat including Senator Day’s chief of staff Rikki Lambert.

“As Senator Day has not formally resigned from the Senate, he maintains the position as a sitting senator and therefore it would be inappropriate to make further comment on this matter.”

Mr Hood said the senator had told colleagues of a “new potential investor” for the housing group.

It is understood liquidators McGrathNicol has received interest in parts of the Home Australia group, but no “white knight” investor has come forward to buy all of it.

It’s been estimated the group owes around $13 million to subcontractors and smaller creditors and has as much as $17 million in bank debt, while the assets are unlikely to fetch more than $6 million.

Senator Day has signed personal guarantees to creditors and admitted he would lose his family home as the creditor liabilities “greatly exceed our assets”.

The Australian constitution bans anyone who is bankrupt or insolvent to sit in parliament.