Two Coalition backbenchers have broken ranks with their government over the "deficit levy", using the Senate debate to register their strong objections to the measure or question its design.

The South Australian Liberal senator, Cory Bernardi, railed against the idea of increasing taxes on people earning more than $180,000, saying he regretted that the Senate debate was "the first opportunity to have a conversation about these tax rates with members of my own party".

The Queensland Liberal National party senator, Ian Macdonald, said he was unhappy the measure was being applied only to individuals rather than being extended to large companies too.

Bernardi told Guardian Australia he intended to abstain if the bill came to a vote, while Macdonald said he was prepared to cross the floor to vote against it, although “it depends on the answers I get to my questions” during the Senate debate.

Both senators acknowledged that crossing the floor would make no difference to the fate of the deficit levy given the Coalition and Labor will vote together to support it.

The open criticism came as the government faced separate accusations from Labor that it was mismanaging the budget process, with the parliament yet to see legislation to give effect to a raft of budget measures due to take effect from 1 July.

The opposition leader, Bill Shorten, said the government was “running scared of its own budget” while Labor’s finance spokesman, Tony Burke, said failing the “competence test”.

The government’s Senate leader, Eric Abetz, told the ABC it stood to reason that not all budget measures would be through the upper house by 1 July, but this was “situation normal”.

“Many a time we have had budget measures being legislated after the event, but the announcement having been made the tax then is collected on the basis that the legislation will verify that tax collection later on,” Abetz said.

On Monday the Senate began debating the "temporary budget repair levy" – which will add 2% on individuals' taxable income above $180,000 a year. The measure – to apply from 1 July for three years – has been touted by the government as a way of ensuring everyone shared in the task of tackling the budget deficit.

The Greens, which oppose the levy in its current form, moved a motion to make it permanent but the amendment failed to secure adequate support. Macdonald was among 58 senators to vote down the Greens’ amendment.

Bernardi, who has previously used his electorate newsletter to criticise the measure, told the Senate the government should be looking to cut taxes, not increase them.

He said people were entitled to keep the vast majority of what they earned and he would like to see more people earning $180,000 or more a year in an "aspirational" society.

"The Australian people are not just economic slaves for government," Bernardi said.

"It's always a difficulty when you're at odds with your own party.

"I regret that this my first opportunity to have a conversation about these tax rates with members of my own party, but on principle I simply am unable to support this. But, like Senator Macdonald, I know the numbers are there. I know that the Labor party and the Coalition will be supporting this bill.

"I don't intend to cross the floor on it but I do want my objection to higher taxes in this country to be registered."

Macdonald said he was inclined to vote against a separate initiative: the government’s paid parental leave scheme.

He acknowledged that his vote on the deficit levy was "going to be fairly irrelevant" in light of the Senate numbers.

"That's why I wanted to take time today to explain my position but not just explain my position, to ask governments in the future, be they Labor or Liberal, if you're going to need extra money have the courage to add a little bit more on the general taxation rate for high income earners. Don't use this levy pretence."

Macdonald said he looked forward to the opportunity to have a discussion with the finance minister, Mathias Cormann, during the Senate debate "so hopefully the minister can explain to me why it is that we tax only individuals and not companies".

Cormann later told the Senate: “Ultimately we as a government have made a judgment and that is what we wanted all Australians, all individuals to contribute to the repair of the budget and of course companies ultimately are made up of individuals.”

He said he did not like increasing tax but Labor left a budgetary “mess” and there was a need “to spread that effort fairly and equitably”.

In Senate question time, the Labor upper house leader, Penny Wong, suggested the government was in “open revolt” and asked “why the Australian people should support a budget that even his own colleagues don't”.

Abetz replied: “The only revoking thing in this chamber is the Labor party’s opposition to our budget measures – their unwillingness to accept the debt and deficit disaster that they left us needs to be fixed up.”

Asked to confirm whether the backbench had not been consulted on key measures, Abetz said the budget went “through all the normal processes”. He said the Coalition was unlike Labor because it embraced a great diversity of points of view.

