Assistant Treasurer Josh Frydenberg has indicated an announcement on the new tax could be made before the budget.
The Government is heading for a fight with the banking industry, which has warned it will have to pass the cost back onto customers.
Mr Frydenberg is a member of the Government's Expenditure Review Committee but has refused to provide any details.
"Any announcements or decisions around this proposed policy which we discussed at the last election will be made in the lead up or on budget night," he said.
Speaking at the Victorian Liberal State Council meeting Mr Abbott has repeated his budget message, focusing on families and small businesses.
"There will be tough decisions in this year's budget as there must be, but there will also be good news."
The banking industry has raised concerns about a deposit tax, saying it will have to pass the cost back onto customers.
Steven Munchenberg from the Australian Bankers' Association said it would be a damaging move for the Government.
"It's going to make it harder for banks to raise deposits which are an important way of funding banks. And therefore for us to fund the economy," he said.
"And we also oppose it because particularly at this point in time with low interest rates a lot of people who are relying on their savings for their incomes are already seeing very low returns and this will actually mean they get even less money."
Bank deposit tax will break election promises: LaborThe Federal Opposition has accused the Government of breaking an election promise by planning to introduce a tax on bank deposits.
The former Labor Government put forward the policy in 2013 to raise revenue for a fund to protect customers in the event of a banking collapse.
Shadow Assistant Treasurer Andrew Leigh said Treasurer Joe Hockey criticised the proposal at the time.
"When we put it on the table Joe Hockey said that it was a smash and grab on Australian households just aimed at repairing the budget," he said.
"I don't think we're going to take any lessons on bipartisanship from Joe Hockey. If he's got any serious proposal to put on the table Labor will respond to that."
abc.net.au 28 Mar 2015
The actions of a fascist dictatorship.
Worse than the so called 'evil' Communism?