Speaking in Canberra on Sunday, Senator Gallagher said while the savings found in a spending audit were worth billions, the final figure would be less than the $22 billion the government found in last October's budget.
"I don't think we'll get to quite where we were in October, it'll be less than that, but it will be significant," she said.
"We've been saying for some time that we will get a significant improvement to the bottom line in the near term."
Senator Gallagher said the government had to find more than $5 billion in the May budget to fund ongoing programs and services.
She described the previous government as "dishonest and dodgy" for not properly funding programs.
"It (the budget) was booby-trapped without a doubt ... it's taken us some time to uncover them," she said.
Asked if the rate of JobSeeker would be lifted, Senator Gallagher said the budget will contain "ongoing" investments to help people with cost-of-living pressures, in addition to one-off measures.
"This budget will have a significant cost-of-living package and that cost-of- living package will be targeted to the most vulnerable Australians," she said.
"That is the core value of the Labor Party and in the Labor government, but it's also about meeting needs across the board."
Senator Gallagher said the budget would continue to support women, but wouldn't confirm if single parents would be allowed to stay at home longer with their children before being moved on to the unemployment payment.
Asked about demands from the Greens, the government freeze rents and interest rates, she said the best way to address the housing crisis would be for the party to back Labor's $10 billion affordable housing fund.
"If the Greens think you can wave a magic wand or snap your finger and solve some of these deeply entrenched issues ... they're wrong, because it's simply not the case," she said.
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