The government’s plans to overhaul its childcare policies will not have an easy ride through the Senate, with the Opposition and Coalition partners the Nationals querying the move.

Nationals senators have warned the government it can’t rely on their vote to pass cuts to the Family Tax Benefit (FTB) as a trade-off for new childcare funding.

Labour and the Greens oppose the FTB cuts and cross bench senators have queried the changes.

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Some Nationals senators have voiced “deep concern” over the scheme’s outcomes for stay-at-home families.

One of the group, Queensland Senator Matthew Canavan said FTB cuts and new childcare funding should not be linked.

“We are deeply concerned about the divide between support for working families and support for families where one parent stays at home … the system we are proposing massively penalises families where a parent stays home to look after children and we think it does not properly value the benefits of unpaid work,” he told the Guardian.

Senator Leyonhjelm thinks family tax benefit cuts don’t go far enough.

He said the government couldn’t count on his vote in the Senate, where they need six cross bench MPs to pass their legislation.

“I’m not ruling anything in or out,” he said. “We’re not going to get walked over, but I don’t take that kind of decision lightly either.”

In a pre-budget announcement, the Treasurer Joe Hockey said new spending on childcare worth $3.5 billion was contingent on cuts to the FTB which have been held up in the Senate since May 2014.

Liberal Democrats Senator David Leyonhjelm said the government was taking an “interesting approach” with the senate, essentially calling on them to choose between the current system and more money for childcare.

“It’s an interesting approach to getting the Senate to realise that you can’t have it all,” he said.

Mr Leyonhjelm supported better targeting of childcare payments but said the cuts do not go far enough.

He said the cuts to the FTB should go through, and to help pay down the deficit no extra money should be allocated to childcare.

“Welfare should be for poor people, not the middle class,” he said.

Family First Senator Bob Day won’t support the trade-off and said he was “very concerned” some would be taxed to pay for subsidies to others.

“The budget direction is fast moving away from tax relief for families, and towards more taxes and then subsidies to those the government of the day wants to support,” he said.