Commendable example-setting of course. But just now the issue isn't so much persuading people to take the vaccine as getting it rolled out fast enough.

The government originally set a target of 4 million people reached by the end March (which slipped to early April). So far, the tally is only something over 100,000 shots.

On Thursday, fronting the Senate's COVID committee, Health Department secretary Brendan Murphy said supply problems had hampered the initial rollout, and could not give a time for reaching the 4 million target.

At the other end of the rollout, some people are expected to be waiting for their second AstraZeneca jab beyond the end of October.

Getting over the initial hurdles and hastening the rollout is one of three challenges Scott Morrison faces right now. The others are managing the economy after JobKeeper's imminent end, and dealing with his ministerial crises - the trickiest of the three, in political terms.

Australia is lucky that, with virtually no current community transmission of COVID-19, this slow start to the vaccination program doesn't present a health threat. But it does mean the removal of remaining restrictions is likely to be held back, and the tardiness leaves Morrison open to criticism.

The PM has always bracketed health and economics in dealing with COVID, and his eyes are now glued to the economy as JobKeeper, the lifeline for so many businesses and workers, finishes in late March.

On the latest figures, at the end of January about 370,000 businesses and 1 million workers were still on JobKeeper. The post-JobKeeper period will be a reckoning point for many enterprises, some of which will go under.

This week Reserve Bank Governor Philip Lowe predicted that "the unemployment rate [currently 6.4 per cent] will continue to trend lower, although this trend could be temporarily interrupted when JobKeeper comes to an end".

In its measures for the post-JobKeeper period, the government has two objectives: to maintain the pace of the recovery, which has been encouragingly strong (3.1 per cent growth in the December quarter), and to help sectors with special problems.

This week it announced assistance for employing apprentices, and help for aviation and tourism. It also extended and expanded the loan scheme for small and medium-sized businesses.

The government can be satisfied the recovery so far is V-shaped, which last year many economists thought improbable.

It is a very different story on the political front, which is chaotic.

Morrison faces a hellish fortnight with parliament's return on Monday. That day, more than 85,000 women are expected to demonstrate in 38 locations around Australia, including outside Parliament House.

The protests have been sparked by Morrison's handling of the two separate allegations of rape that have consumed federal politics for weeks. The demonstrators' broader themes are that women must be heard and believed, and they must be safe.

Neither Attorney-General Christian Porter nor Defence Minister Linda Reynolds will be there to see the Canberra women. He's on mental health leave; she's on medical leave. But the government is certain to be pummelled with questions in parliament about them both.

Morrison has yet to reveal the results of the inquiry by his departmental secretary, Phil Gaetjens, into who of his staff knew what when about Brittany Higgins' allegation she was raped in Reynolds' office in 2019.

And Reynolds' "lying cow" comment will no doubt get a run. Reynolds now has to pay out money to Higgins over the comment; Higgins is giving it to a Canberra organisation that helps rape victims.

Porter remains Morrison's most serious political problem, going to what standards should be demanded for the occupant of the position of the country's first law officer.

On Friday Macquarie Group senior managing director James Hooke, a former boyfriend of the now deceased woman, said in a statement he'd had "relevant discussions" with both her and Porter and would co-operate with an inquiry.

Morrison this week was firmly dug in behind Porter, despite his being highly damaged political goods.

Government sources insist Morrison, and other colleagues, want Porter back in his job - they are afraid of the precedent set if he leaves the ministry.

This ignores the fact that, on any commonsense view, this is surely a one-off ministerial situation.

On the other hand, Morrison's preference would probably be for Reynolds to step down, citing her health - but that decision remains in her hands.

The PM is assuming these ministerial crises will blow over soon enough.

He may accept that many people (especially women) will have strong views on the issues - the "toxic" Parliament House culture, the suitability of Porter for office, how the government handles matters affecting women. But he'd calculate these aren't substantial vote-changers.

That may be right. Or it might be dangerous complacency.

Although Morrison has a big lead as preferred PM, the poll numbers are tight, and the government has no electoral fat for the contest that's little more than a year away at most. Also, for as long as the ministerial crises are front and centre, the Coalition can't get its messages out properly.

By early May, Morrison needs to have the vaccine rollout marching at a good clip, the economic recovery coping with the end of JobKeeper, and Porter and Reynolds no longer damaging distractions.

That would give him a good run into the budget.

Not much to ask, really.