The High Court is considering the eligibility of Mr Day to run for the Senate in July last year.

The make-up of the Senate hangs on the outcome, with the government requiring the support of eight of the nine remaining crossbenchers to pass legislation if Labor and the Greens combine to oppose them, now that two former senators are being scrutinised by the High Court.

The High Court is also reserving its judgment on the eligibility of former One Nation Senator Rod Culleton to run for the Senate.

If the court decides Mr Day was validly elected before he resigned in late last year, his replacement would be decided by a joint sitting of the South Australian Parliament, which would likely endorse another Family First candidate.

But if he was not eligible to run for the Senate, the High Court could order a recount, which could alter the course of the Senate. Ms McEwen's team hope this would open the way for her to return to Parliament.

At a directions hearing on Tuesday, Ms McEwen's lawyers made an 11th-hour bid to introduce new evidence they said would show that if Mr Day had not been on the ballot paper and "distorted" the outcome, Ms McEwen could have won.

Ms McEwen, who lost out to Mr Day at the 2016 election, is a party to the High Court challenge against his eligibility to be a senator.

Her barrister, Simona Gory, told Justice Gordon that the key would be whether Senator Day's election had been built on the "distortion" of him being on the ballot paper under the Family First banner.

She argued that Mr Day's inclusion on the ballot paper as a Family First candidate had inflated the party's vote to such a degree that Ms McEwen might have been elected if it weren't for Mr Day.

"The stakes are very high in this case," Ms Gory told the court.

"The answer will determine who is the elected representative of the people of South Australia . . . and it will determine the executive branch of the federal government . . . this is a case in the highest public interest."

The stoush centres on whether Mr Day had a financial interest in the building where his Adelaide parliamentary office was located.

The Senate referred the matter to the High Court late last year, to decide whether Mr Day's election was in breach of section 44 of the constitution – rules that make it illegal for members of Parliament to receive ­"indirect pecuniary interests" from the Commonwealth.

But High Court Justice Michelle Gordon on Tuesday ruled out Ms McEwen's bid to introduce as evidence political analysis of the election results data compiled by University of Sydney political scientist Simon Jackman.

Justice Gordon said Ms McEwen's team had sought to argue that any Family First votes cast above the line on the Senate ballot paper, and any votes for Mr Day below the line, should be discounted and that political advertising featuring Mr Day could have compelled people to vote for the Family First party.

It was, Justice Gordon said, an advocacy for a "pure personality" view of politics, which was at odds with Australia's representational style of politics.

She was particularly scathing of Ms McEwen's legal team for introducing their application to have the report used as evidence in the hearing at such a late stage.

Late last year, Justice Gordon set a deadline of December 16 for all parties to provide their witness lists and all other correspondence they would rely on to each other and to the court.

Despite this, she said, Ms McEwen's legal team did not file the Jackman report with the court until January 13, which she described as a "failure to comply with court orders".

Justice Gordon granted an application for costs by lawyers for Attorney General George Brandis, and Mr Day, against Ms McEwen.

The hearing will begin on Monday.

- with AAP