Labor is leading the race to form a minority government, holding 74 of the required 76 lower house seats.
That is one more than the coalition has managed to secure.
It's now up to the three rural independents to decide whether Prime Minister Julia Gillard stays in the top job, or Opposition Leader Tony Abbott takes over the reins.
Independent Tony Windsor said he and his colleagues Bob Katter and Rob Oakeshott wanted to meet with both leaders again today, before making their final decision on whom to back.
"My guess is that on the basis of all of that we'll make a determination probably tomorrow morning," he told ABC Radio.
But Mr Windsor wouldn't rule out a decision sooner.
"Anything can happen," he said.
Mr Windsor is hoping the trio all choose the same party, so a 75-all outcome - and an early election - can be avoided.
"I'd hope that we'd all vote in a similar fashion, but there is no guarantee of that at all," he said.
"People may be leaning one way, but they may have to come back the other way to get some stability into the system."
Mr Oakeshott said the three men had a "full spread" of political and policy views but were willing to put them aside to avoid a stalemate.
"The three of us have talked about that a lot," he told reporters outside Parliament House.
"There is a national interest issue in question about how we have a stable government over the next three years."
Mr Oakeshott wouldn't speculate on the outcome of fresh talks with Ms Gillard and Mr Abbott.
"We'll just see how today unfolds and see what sort of final offers are made by both parties," he said.
Meanwhile, Mr Katter revealed he recently lunched with Opposition Leader Tony Abbott's chief of staff, and Liberal senator Bill Heffernan.
But he warned that meeting should not be overemphasised, as he'd also been around to former Labor prime minister Kevin Rudd's home twice lately.
