Treasurer Scott Morrison wants his seven-year personal income tax cut plan passed by the parliament as one package, but Labor has already indicated it will only support the first stage.
Mr Morrison presented the three-part plan to parliament on Wednesday and wants the key part of Tuesday's budget passed by both houses by June.
"I think the Australian people for whom this tax relief is designed for would expect the parliament to do its job and get this tax relief to them," he told the National Press Club during his traditional post-budget address.
Parliament will rise on Thursday after its three-day sitting week for the budget and the lower house will return in the final two weeks of May.
But the Senate won't sit again until June 18 because of estimates hearings in the interim.
The tax cuts, which include from July 1 a low and middle-income tax offset of up to $530, will cost $13.4 billion over the first four years and the whole package will amount to $140 billion over a decade.
But Mr Morrison has repeatedly declined requests from Labor to break down the year-by-year cost beyond the first four years, saying it is not standard practice because estimates are unreliable.
Also from July 1, the 32.5 per cent tax bracket threshold will be increased to $90,000, from $87,000, which save 210,000 people from having to pay 37 cents in the dollar due to bracket creep.
More changes are planned in 2024/25, when the government proposes abolishing the 37 per cent tax bracket altogether.
Opposition Leader Bill Shorten argued the government wants to debate a tax cut that is two or three elections down the track.