Kuenssberg: Sunak is now hostage to his promises on childcare and small boats

"You can get a lot done in a week" - a snap from Rishi Sunak's oh-so-casually put-together social media feed shows him sitting on a bench, reading through his notes on the tarmac near a couple of parked-up fighter jets.

The stream of images is designed to show the world a few days of frenetic activity. Here I am with Joe Biden! Here I am at the Budget! Here I am working as hard as I can on your behalf!

During his first couple of months in charge Rishi Sunak's workaholic tendencies were applied to a set of acute and immediate problems - could he stop the turmoil in the Tory Party and the financial markets? Then, did he have a clear idea of what he wanted to get done?

He tried to answer that with his five pledges at the turn of the year. Allies say there's a "chipper mood" and a sense now he can start to focus on priorities he chooses, rather than mop up the mess of what happened before.

But here's the next challenge - can Rishi Sunak make what he has promised to voters a reality?

Carefully crafted social media images aim to show the world Rishi Sunak's frenetic activity

The Budget was, one government insider said, "all right, given we had no money". Budgets sometimes unravel in a mess in the days that follow them - remember George Osborne's "omnishambles", or Philip Hammond's breach of the Conservative manifesto on National Insurance rises that he had to ditch?

That hasn't happened this time. In fact, one former minister branded it a "snoozefest". But that doesn't mean it's trouble-free. The idea designed to catch the eye of most voters is also a massive logistical task.

Giving hard-pressed parents a lot more support sounds appealing and could make a practical difference to many voters' lives. From a purely political point of view it also has an allure for Tory HQ, because childcare was an issue where Labour was trying to make the running.

But what ministers have branded the "biggest-ever expansion on childcare" in England could be extremely hard to make happen. Nurseries have been closing in recent years, as they find it harder and harder to make childcare viable as a business.

Ministers are aware that it could be a stretch: that is why the changes are being phased in gradually. But if the promise of more gleaming nurseries, happy toddlers and less-stressed parents is not matched by reality, the government may be punished.

There's a strand of Conservative opinion uneasy with what amounts to another expensive expansion of the state.

And don't forget the big picture - the Budget pointed to the pressure on people's wallets, with living standards dropping and fears of a "lost decade". A big, expensive promise on childcare that's hard to keep doesn't erase that reality overnight.

Chancellor Jeremy Hunt pledged a big increase in childcare, but nurseries have been closing

The prime minister has also piled huge amounts of political effort into ending the passage of migrants across the Channel.

The slogan, "Stop the Boats", even appears on his government lectern. This simple three-word phrase, lifted from Australia, has already become part of the political lexicon.

The home secretary has just touched down in Rwanda where she hopes to push on with efforts to have migrants who arrive in the UK sent there. Almost every time a government minister opens their mouth they mention the steps they are taking, more new laws that have just started to make their way through Parliament this week, notwithstanding the doubts expressed by some senior Conservatives, even Theresa May.

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But keeping that vow to end the crossings will be extremely difficult. The courts soon have another say over the legality of sending new arrivals to Rwanda. The practicalities of where anyone detained will be housed are unclear.

Relations with France are on a much better footing with "le bromance" between Rishi Sunak and President Emmanuel Macron. But France has not signed up to a returns agreement. It is impossible to know if Rishi Sunak's promise will make very much difference.

A sceptic might suggest that ministers are aware of that, and being seen to make an effort also matters. The party's strong language on immigration also is a point of contrast with the Labour Party. Yet - just as with the big offer on free childcare - a promise made, but not kept, could be intensely damaging.

For a leader who favours under-promising and over-delivering, Rishi Sunak has set the government two very significant tasks, neither of which he can be sure of achieving. In the coming weeks, there'll be more - new measures to tackle anti-social behaviour, a push on green business, and possibly plans for local healthcare too.

The French president hailed a "moment of reconnection", but there was no deal on returning migrants across the Channel

His supporters reckon the prime minister now has his own momentum, an elusive element in politics that is hard to create. But there are banana skins that could cause the calm to slip in the coming days.

His old boss will be in front of MPs answering questions on the toxic mess of Partygate. Like it or not, Boris Johnson is a walking, talking headline-generator, who sucks up nearly all available political oxygen.

One minister told me the "'bring back Boris' brigade are more muted now", but his presence is always unpredictable and disruptive, a headache the current No 10 could do without.

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More seriously, this week there is a vote on what the prime minister hailed as a genuine breakthrough, the Windsor Framework, to unpick the long-standing knot of the Northern Irish Protocol.

The Northern Irish unionists, the DUP, who have long objected to the effects the arrangements have, are yet to reveal exactly what they will do. They are not big in number, but their support - or lack of it - is fundamental to whether government can get up and running in Northern Ireland again.

For all that Rishi Sunak's allies and many Conservative MPs reckon his approach is starting to work, there's not much evidence of it in the polls, which remain stubbornly appalling for the Conservatives. But polls aren't real votes.

It's not long now until the prime minister faces the most important verdict of all and his first in the job - local elections at the ballot box in May. Then his promises, and the public's belief that he can keep them, will be put to the test for real.