The federal government could have major problems getting its legislation passed in the Senate amid revelations Family First senator Bob Day may have been invalidly elected.

The High Court may be asked to consider whether Mr Day’s election to the upper house was a breach of the constitution, potentially forcing a recount of the South Australian Senate vote.

The result of a recount is anyone’s guess, and a High Court decision is expected to take weeks.

Mr Day almost always voted with the government on legislation and motions, providing a crucial vote until he quit on Tuesday morning, effective immediately.

It was believed he’d be replaced by a Family First candidate but that’s been thrown into doubt after Senate President Stephen Parry revealed there were “difficult constitutional questions” following his resignation.

Attorney-General George Brandis says the government will ask the Senate to refer the matter to the High Court on Monday.

He says Special Minister of State Scott Ryan wrote to Senator Parry and Mr Day last week to raise concerns about a potential indirect pecuniary interest Senator Day had in a contract with the commonwealth.

It’s believed Senator Day’s taxpayer-funded Adelaide electorate office was in a building in which he had a financial interest.

That could put him in breach of section 44 of the constitution, which states that any person with any direct or indirect pecuniary interest in any agreement with the commonwealth – except as part of a company with more than 25 people – “shall be incapable of being chosen or of sitting as a senator or a member of the House of Representatives”.

In a statement, Family First said it had no prior knowledge of the allegations and was seeking legal advice.

“Mr Day has denied that any pecuniary interest exists or had existed,” it said.

UNSW constitutional law expert Professor George Williams said if the High Court determines Mr Day was ineligible to have been elected, it could order a recount.

“The High Court will want to resolve this quickly, particularly given the closeness of the votes in the Senate,”.

If Mr Day was deemed ineligible, ABC election analyst Antony Green says the court would then need to decide whether the entire Family First ticket was eligible.

“If Family First’s entire ticket were excluded in a SA Senate recount, last spot would be a race between Labor and One Nation,” he tweeted.

The government has 30 out of 76 seats in the Senate.

Without the support of Labor or the Greens, it needs the votes of nine out of 11 crossbenchers.

Leader of the opposition in the Senate Penny Wong said Labor would take independent legal advice, including whether it was desirable to refer the matter to the High Court.

Mr Day’s Home Australia group of companies has been placed into liquidation, halting construction on 207 new homes in SA, Western Australia, Queensland, Victoria and NSW.

He announced last month he would quit the Senate because of financial problems with the business but was hopeful last week of seeing out his parliamentary term if an investor could revive his housing group.

He said he would attend the parliamentary sitting starting Monday to support bills allowing a same-sex marriage plebiscite and reinstating the building industry watchdog.

He resigned on Tuesday after a major investor that had been examining his failed business decided not to proceed.