The prime minister stressed the need to exercise "fiscal discipline" in a speech to the National Press Club on Monday.
"You can't run the Australian economy on taxpayers' money forever," Mr Morrison said.
"We are not running a blank cheque budget."
There are still about 500,000 businesses receiving JobKeeper and it is unclear how many will fold when the scheme comes to an end.
It is also unclear what will happen to more than one million people on JobSeeker payments once coronavirus supplements expire on March 31.
Without government intervention, the unemployment benefit will return to just $40 a day.
Mr Morrison is monitoring the unemployment and workforce participation rates as he keeps people in suspense.
"One thing I've learnt over the course of the last 12 months is in a pandemic, don't get too far ahead of yourself. Things have a habit of changing on you, and that is true here," he said.
"We haven't made any agreement yet, but we will look at the need to have people in jobs, because you will always get paid more in jobs than you will on a benefit.
"At least, that's how it should be."
Opposition Leader Anthony Albanese is open to reining in government spending, so long as the right purse strings are pulled.
Mr Albanese argues government stimulus programs have been ill-directed and plagued by waste.
He claims there is nothing to show for the unprecedented spending blitz.
"The problem here is not that there has been spending - that was needed during a crisis, as it was needed during the Global Financial Crisis," Mr Albanese told ABC radio.
"The problem here is you have a trillion dollars of debt with nothing to show for it."
The opposition leader downplayed the 6.6 per cent unemployment rate, which is better than global standards, and Australia's strong economic growth.
"What's the economic reform or legacy arising out of this? That's the question," he said.
This government doesn't have a major infrastructure project, they don't have a major economic reform, they won't have any legacy from this trillion dollars in debt, which does have to be paid back.
The prime minister refused to commit to clawing back JobKeeper payments from companies that have handed out executive bonuses and paid dividends to their shareholders.
"I'm not into the politics of envy - I'll leave that to my opponents," he said.
Mr Morrison is still considering tailored support for the hardest hit industries once JobKeeper is cut off.
Treasury is analysing tourism industry data and talks are under way with industry leaders to consider assistance measures, with many businesses under pressure from the closure to international visitors.
But Mr Morrison says any emergency measures will be temporary and accompanied by a "clear fiscal exit strategy".
WHAT's ON THE AGENDA FOR THE FIRST WEEK OF PARLIAMENT
* House and Senate sitting from Tuesday to Thursday;
* Scott Morrison and Anthony Albanese have reshuffled their front bench teams since parliament rose in December;
* Coronvirus pandemic continues, meaning some restrictions apply in Parliament House, but there have been no local cases in Australia for a fortnight;
* Church service to be held in Canberra on Tuesday morning to open the parliamentary year;
* Labor is set to pursue the government over its handling of the JobKeeper wage subsidy rollout and its lack of commitment to ambitious action on climate change;
* Government legislation in the Senate dealing with home care payment system, native title, mandatory credit reporting, higher education, redress scheme, radioactive waste management;
* Legislation in the House: aged care serious incident response scheme, banking royal commission measures, freedom of speech in universities, Clean Energy Finance Corporation grid reliability fund;
* Senate inquiry report to be presented on issues facing diaspora communities in Australia;
* Condolence motion on Tuesday over the death of former governor general Michael Jeffery;
* Just after parliament rises, economics committee on Friday will quiz Reserve Bank governor Philip Lowe.