As shell-shocked Liberal MPs struggled to accept the sudden resignation of Barry O’Farrell on Thursday, talk turned to how new Premier Mike Baird would work with his federal colleagues.

Baird holds the state seat of Manly, which sits within Prime Minister Tony Abbott’s federal seat of Warringah. The pair are both surfers – they’ve actually surfed together – and are family men with a strong Christian faith (Abbott trained to be a priest; Baird hoped to become a missionary).

In Baird, Abbott and federal Treasurer Joe Hockey have a political soul mate who could help them realise their plans to rebuild NSW.

The 56-year-old Abbott has worked in the cut and thrust of politics since the early 1990s, when he served as press secretary to former opposition leader John Hewson.

In comparison, Baird, 44, is a relatively recent arrival on the political stage, having been elected only in 2007. But the former HSBC executive has been in and around politics for much of his life – his father Bruce served in the state and then federal parliaments from 1984 to 2007. And it was against his father’s advice that he entered public life.

Liberal insiders rushed to emphasise the strength of the relationship between Abbott and Baird on Thursday. And the new Premier’s elevation is a chance for the relationship between the federal and state governments to be reset.

Abbott and O’Farrell were not always on the same political page, including when O’Farrell ensured NSW was the first state to sign up to the former Gillard government’s Gonski reforms.

Baird’s political leanings are in line with those of Hockey. The 49-year-old Hockey is said to be delighted with Baird’s appointment, as well as that of his deputy Gladys Berejiklian, with whom Hockey is particularly close.

Hockey and Baird have a similar economic rationalist view of the world. There is renewed optimism in Liberal ranks that the elevation of Baird will restart the push to privatise NSW’s electricity poles and wires.

As treasurer, Baird oversaw the sale of Port Botany and Port Kembla, and such a sale could reap $30 billion in revenue. If it were to be ploughed back into infrastructure, as seems likely, Hockey and Abbott would be delighted.

Abbott has promised to be an “infrastructure prime minister”, while Hockey is driving the government’s push to recycle old or “brownfields” infrastructure to fund new projects.

On Thursday, just days after the announcement that Badgerys Creek would be the venue for Sydney’s second airport, and that billions would be spent on roads to support it, Baird spoke about the “huge infrastructure backlog” facing NSW when the Coalition came to office.

He pledged his next budget, just weeks away, would continue to tackle the problem. Abbott and Hockey would have been thrilled.

Triumvirate have similar views on state