But Ms O'Dwyer, the minister for revenue and financial services, says the banks, like other businesses benefiting from a tax cut, would invest and innovate in their companies and make sure they can employ people.
"We're going to have a new taxation system that's based on a morality tax? I mean, let's get a little bit real here," she told ABC television on Sunday.
But Senator Hinch is sticking to his guns, saying he will support tax cuts for companies with a turnover of up to $500 million - like the Senate did for firms with a turnover of up to $50 million last year.
"But will not reward corrupt banks being exposed daily in the royal commission. That is a pledge," he said in a tweet on Sunday.
Opposition Leader Bill Shorten took to Facebook with a new attack ad, saying: "(Malcolm) Turnbull wanted to protect the banks. Now he wants to give them a big tax handout."
The government delayed putting the remainder of the legislation to the vote in the Senate just before Easter when it became clear it didn't have sufficient numbers from the crossbench to pass it.
Senator Hinch and fellow independent Tim Storer have so far rejected the plan, joining Labor, the Greens and senators of the previously named Nick Xenophon Team.
So far, only firms with a turnover of up to $50 million will receive incremental tax cuts over the next decade from 30 per cent to 25 per cent.
Opposition finance spokesman Jim Chalmers said Ms O'Dwyer's comments show she was "spectacularly out of touch".
He said Labor analysis found the big four banks at the centre of "rorts, rip-offs and scandals" exposed by the royal commission would reap $13.2 billion under the government's 10-year business tax plan.
It shows the banks will receive one in every four dollars of the $65 billion tax cut once it is fully implemented in 2026/27.
The Commonwealth Bank of Australia would receive a tax cut of almost $4 billion while Westpac would pocket 3.5 billion, the ANZ $3.2 billion and National Australia Bank $2.6 billion.
Labor wants the government to ditch all the unlegislated parts of the tax plan which are in front of the parliament.
"We don't think it is a good time to shower largesse on multinationals and millionaires, but especially when we've got record and growing debt in the budget," Dr Chalmers told ABC television.